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Preprints:

J. Kuneš, I. Leonov, P. Augustinský, V. Křápek, M. Kollar, and D. Vollhardt,
LDA+DMFT approach to ordering phenomena and the structural stability of correlated materials,
[arXiv:1705.00875].
Materials with correlated electrons often respond very
strongly to external or internal influences, leading to
instabilities and states of matter with broken
symmetry. This behavior can be studied theoretically either
by evaluating the linear response characteristics, or by
simulating the ordered phases of the materials under
investigation. We developed the necessary tools within the
dynamical meanfield theory (DMFT) to search for electronic
instabilities in materials close to spinstate crossovers
and to analyze the properties of the corresponding ordered
states. This investigation, motivated by the physics of
LaCoO_{3}, led to a discovery of condensation of
spinful excitons in the twoorbital Hubbard model with a
surprisingly rich phase diagram. The results are reviewed in
the first part of the article. Electronic correlations can
also be the driving force behind structural transformations
of materials. To be able to investigate correlationinduced
phase instabilities we developed and implemented a formalism
for the computation of total energies and forces within a
fully charge selfconsistent combination of density
functional theory and DMFT. Applications of this scheme to
the study of structural instabilities of selected correlated
electron materials such as Fe and FeSe are reviewed in the
second part of the paper.
Published:

E. Canovi, M. Kollar, and M. Eckstein,
Stroboscopic prethermalization in weakly interacting periodically driven systems,
Phys. Rev. E 93, 012130 (2016)
[ PDF / AIP 2016 ].
[arXiv:1507.00991]
Timeperiodic driving provides a promising route toward
engineering nontrivial states in quantum manybody
systems. However, while it has been shown that the dynamics of
integrable, noninteracting systems can synchronize with the
driving into a nontrivial periodic motion, generic
nonintegrable systems are expected to heat up until they
display a trivial infinitetemperature behavior. In this paper
we show that a quasiperiodic time evolution over many periods
can also emerge in weakly interacting systems, with a clear
separation of the timescales for synchronization and the
eventual approach of the infinitetemperature state. This
behavior is the analog of prethermalization in quenched
systems. The synchronized state can be described using a
macroscopic number of approximate constants of motion. We
corroborate these findings with numerical simulations for the
driven Hubbard model.

D. Braak, J. M. Zhang, and M. Kollar,
Integrability and weak diffraction in a twoparticle BoseHubbard model,
J. Phys. A: Math. Theor. 47, 465303 (2014).
[arXiv:1403.6875]
A recently introduced onedimensional twoparticle
BoseHubbard model with a single impurity is studied on finite
lattices. The model possesses a discrete reflection symmetry
and we demonstrate that all eigenstates odd under this
symmetry can be obtained with a generalized Bethe ansatz if
periodic boundary conditions are imposed. Furthermore, we
provide numerical evidence that this holds true for open
boundary conditions as well. The model exhibits backscattering
at the impurity site  which usually destroys integrability
 yet there exists an integrable subspace. We investigate the
nonintegrable even sector numerically and find a class of
states which have almost the Bethe ansatz form. These weakly
diffractive states correspond to a weak violation of the
nonlocal YangBaxter relation which is satisfied in the odd
sector. We bring up a method based on the Prony algorithm to
check whether a numerically obtained wave function is in the
Bethe form or not, and if so, to extract parameters from
it. This technique is applicable to a wide variety of other
lattice models.

H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner,
Nonequilibrium dynamical meanfield theory and its applications,
Rev. Mod. Phys. 86, 779 (2014)
[ PDF / AIP 2014 ].
[arXiv:1310.5329].
The study of nonequilibrium phenomena in correlated lattice
systems has developed into one of the most active and exciting
branches of condensed matter physics. This research field
provides rich new insights that could not be obtained from the
study of equilibrium situations, and the theoretical
understanding of the physics often requires the development of
new concepts and methods. On the experimental side, ultrafast
pumpprobe spectroscopies enable studies of excitation and
relaxation phenomena in correlated electron systems, while
ultracold atoms in optical lattices provide a new way to
control and measure the time evolution of interacting lattice
systems with a vastly different characteristic time scale
compared to electron systems. A theoretical description of
these phenomena is challenging because, first, the
quantummechanical time evolution of manybody systems out of
equilibrium must be computed and second, strongcorrelation
effects which can be of a nonperturbative nature must be
addressed. This review discusses the nonequilibrium extension
of the dynamical mean field theory (DMFT), which treats
quantum fluctuations in the time domain and works directly in
the thermodynamic limit. The method reduces the complexity of
the calculation via a mapping to a selfconsistent impurity
problem, which becomes exact in infinite
dimensions. Particular emphasis is placed on a detailed
derivation of the formalism, and on a discussion of numerical
techniques, which enable solutions of the effective
nonequilibrium DMFT impurity problem. Insights gained into the
properties of the infinitedimensional Hubbard model under
strong nonequilibrium conditions are summarized. These
examples illustrate the current ability of the theoretical
framework to reproduce and understand fundamental
nonequilibrium phenomena, such as the dielectric breakdown of
Mott insulators, photodoping, and collapseandrevival
oscillations in quenched systems. Furthermore, remarkable
novel phenomena have been predicted by the nonequilibrium DMFT
simulations of correlated lattice systems, including dynamical
phase transitions and fieldinduced repulsiontoattraction
conversions.

J. M. Zhang and M. Kollar,
Optimal multiconfiguration approximation of an Nfermion wave function,
Phys. Rev. A 89, 012504 (2014)
[ PDF / AIP 2014 ].
[arXiv:1309.1848].
We propose a simple iterative algorithm to construct the
optimal multiconfiguration approximation of an Nfermion wave
function. Namely, M>=N singleparticle orbitals are sought
iteratively so that the projection of the given wave function
in the C^{N}_{M}dimensional configuration
subspace is maximized. The algorithm has a monotonic
convergence property and can be easily parallelized. The
significance of the algorithm on the study of geometric
entanglement in a multifermion system and its implication on
the multiconfiguration timedependent HartreeFock (MCTDHF)
are discussed. The ground state and realtime dynamics of
spinless fermions with nearestneighbor interaction are
studied using this algorithm, discussing several subtleties.

C. Gramsch, K. Balzer, M. Eckstein, and M. Kollar,
Hamiltonianbased impurity solver for nonequilibrium dynamical meanfield theory,
Phys. Rev. B 88, 235106 (2013)
[ PDF / AIP 2013 ].
[arXiv:1306.6315].
We derive an exact mapping from the action of nonequilibrium
dynamical meanfield theory (DMFT) to a singleimpurity
Anderson model (SIAM) with timedependent parameters, which
can be solved numerically by exact diagonalization. The
representability of the nonequilibrium DMFT action by a SIAM
is established as a rather general property of nonequilibrium
Green functions. We also obtain the nonequilibrium DMFT
equations using the cavity method alone. We show how to
numerically obtain the SIAM parameters using Cholesky or
eigenvector matrix decompositions. As an application, we use a
Krylovbased time propagation method to investigate the
Hubbard model in which the hopping is switched on, starting
from the atomic limit. Possible future developments are
discussed.

M. Greger, M. Kollar, and D. Vollhardt,
Isosbestic points: How a narrow crossing region of curves determines their leading parameter dependence,
Phys. Rev. B 87, 195140 (2013)
[ PDF / AIP 2013 ].
[arXiv:1212.4980]
We analyze the sharpness of crossing ("isosbestic") points
which are observed in many quantities described by a function
f(x,p), where x is a variable (e.g., the frequency) and p a
parameter (e.g., the temperature). We derive a simple
criterion that needs to be fulfilled by f(x,p) to exhibit a
sharp isosbestic point and relate it to the applicability of
perturbation theory in p. Using this approach we explain the
sharpness of crossing points in the optical conductivity
sigma(ω,n) of the FalicovKimball model and the spectral
function A(ω,U) of the Hubbard model. We also analyze
isosbestic points in data for the Raman response
chi(ω,T) of HgBa_{2}CuO_{4+δ},
photoemission spectra I(ω,T) of thin VO_{2}
films, and the reflectivity R(ω,T) of
CaCu_{3}Ti_{4}O_{12}.

F. A. Wolf, F. Vallone, G. Romero, M. Kollar, E. Solano, and D. Braak,
Dynamical correlation functions and the quantum Rabi model,
Phys. Rev. A 87, 023835 (2013)
[ PDF / AIP 2013 ].
[arXiv:1211.6469]
We study the quantum Rabi model within the framework of the
analytical solution developed in Phys. Rev. Lett. 107,100401
(2011). In particular, through timedependent correlation
functions, we give a quantitative criterion for classifying
two regions of the quantum Rabi model, involving the
JaynesCummings, the ultrastrong, and deep strong coupling
regimes. In addition, we find a stationary qubitfield
entangled basis that governs the whole dynamics as the
coupling strength overcomes the mode frequency.

J.M. Zhang, D. Braak, and M. Kollar
Bound states in the onedimensional twoparticle Hubbard model with an impurity,
Phys. Rev. A 87, 023613 (2013)
[ PDF / AIP 2013 ].
[arXiv:1210.6767]
We investigate bound states in the onedimensional
twoparticle BoseHubbard model with an attractive (V>0)
impurity potential. This is a onedimensional, discrete
analogy of the hydrogen negative ion H^ problem. There are
several different types of bound states in this system, each
of which appears in a specific region. For given V, there
exists a (positive) critical value U_{c1} of U, below which
the ground state is a bound state. Interestingly, close to the
critical value (U<~U_{c1}), the ground state can be
described by the Chandrasekhartype variational wave function,
which was initially proposed for H^. For U>U_{c1}, the
ground state is no longer a bound state. However, there exists
a second (larger) critical value U_{c2} of U, above which a
moleculetype bound state is established and stabilized by the
repulsion. We have also tried to solve for the eigenstates of
the model using the Bethe ansatz. The model possesses a global
Z_2symmetry (parity) which allows classification of all
eigenstates into even and odd ones. It is found that all
states with oddparity have the Bethe form, but none of the
states in the evenparity sector. This allows us to identify
analytically two oddparity bound states, which appear in the
parameter regions 2V<U<V and V<U<0,
respectively. Remarkably, the latter one can be
embedded in the continuum spectrum with appropriate
parameters. Moreover, in part of these regions, there exists
an evenparity bound state accompanying the corresponding
oddparity bound state with almost the same energy.

M. Greger, M. Kollar, and D. Vollhardt,
Emergence of a common energy scale close to the orbitalselective Mott transition,
Phys. Rev. Lett. 110, 046403 (2013)
[ PDF / AIP 2013 ].
[arXiv:1205.5782]
We calculate the spectra and spin susceptibilities of a
Hubbard model with two bands having different bandwidths but
the same onsite interaction, with parameters close to the
orbitalselective Mott transition, using dynamical meanfield
theory. If the Hund's rule coupling is sufficiently strong,
one common energy scale emerges which characterizes both the
location of kinks in the selfenergy and extrema of the
diagonal spin susceptibilities. A physical explanation of this
energy scale is derived from a Kondotype model. We infer that
for multiband systems local spin dynamics rather than
spectral functions determine the location of kinks in the
effective band structure.

J.M. Zhang, D. Braak, and M. Kollar
Bound states in the continuum realized in the onedimensional twoparticle Hubbard model with an impurity,
Phys. Rev. Lett. 109, 116405 (2012)
[ PDF / AIP 2012 ].
[arXiv:1205.6431]
We report a bound state of the onedimensional twoparticle
(bosonic or fermionic) Hubbard model with an impurity
potential. This state has the Betheansatz form, although the
model is nonintegrable. Moreover, for a wide region in
parameter space, its energy is located in the continuum
band. A remarkable advantage of this state with respect to
similar states in other systems is the simple analytical form
of the wave function and eigenvalue. This state can be tuned
in and out of the continuum continuously.

F. A. Wolf, M. Kollar, and D. Braak
Exact realtime dynamics of the quantum Rabi model,
Phys. Rev. A 85, 053817 (2012)
[ PDF / AIP 2012 ].
[arXiv:1203.6039]
We use the analytical solution of the quantum Rabi model to
obtain absolutely convergent series expressions of the exact
eigenstates and their scalar products with Fock states. This
enables us to calculate the numerically exact time evolution
of <σ_{x}(t)> and
<σ_{z}(t)> for all regimes of the coupling
strength, without truncation of the Hilbert space. We find a
qualitatively different behavior of both observables which can
be related to their representations in the invariant parity
subspaces.

D. Vollhardt, K. Byczuk, and M. Kollar,
Dynamical MeanField Theory,
in: Strongly Correlated Systems,
ed. by A. Avella and F. Mancini, Springer Series in SolidState Sciences (Springer Berlin Heidelberg, 2011), Vol. 171, p. 203236
[arXiv:1109.4833].
The dynamical meanfield theory (DMFT) is a widely
applicable approximation scheme for the investigation of
correlated quantum manyparticle systems on a lattice,
e.g., electrons in solids and cold atoms in optical
lattices. In particular, the combination of the DMFT with
conventional methods for the calculation of electronic
band structures has led to a powerful numerical approach
which allows one to explore the properties of correlated
materials. In this introductory article we discuss the
foundations of the DMFT, derive the underlying
selfconsistency equations, and present several
applications which have provided important insights into
the properties of correlated matter.

M. Kollar,
Introduction to Dynamical MeanField Theory,
in: The LDA+DMFT approach to strongly correlated materials,
ed. by E. Pavarini, E. Koch, D. Vollhardt, and A. I. Lichtenstein, Chapter 5 (Forschungszentrum Jülich, 2011)
[PDF at fzjuelich.de].

P. van Dongen, M. Kollar, and T. Pruschke (eds.),
Electronic Correlations in Models and Materials (Special Topic Issue),
Ann. Phys. 523 (89), 583758 (2011).
Preface.

M. Kollar, F. A. Wolf, and M. Eckstein,
Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems,
Phys. Rev. B 84, 054304 (2011)
[ PDF / AIP 2011 ].
Selected for PRB Editors' Suggestions.
[arXiv:1102.2117]
A quantum manybody system which is prepared in the ground
state of an integrable Hamiltonian does not directly
thermalize after a sudden small parameter quench away from
integrability. Rather, it will be trapped in a
prethermalized state and can thermalize only at a later
stage. We discuss several examples for which this
prethermalized state shares some properties with the
nonthermal steady state that emerges in the corresponding
integrable system. These examples support the notion that
nonthermal steady states in integrable systems may be
viewed as prethermalized states that never decay
further. Furthermore we show that prethermalization
plateaus are under certain conditions correctly predicted
by generalized Gibbs ensembles, which are the appropriate
extension of standard statistical mechanics in the presence
of many constants of motion. This establishes that the
relaxation behaviors of integrable and nearly integrable
systems are continuously connected and described by the
same statistical theory.

A. P. Kampf, M. Kollar, J. Kuneš, M. Sentef, and D. Vollhardt,
MaterialSpecific Investigations of Correlated Electron Systems,
in: High Performance Computing in Science and Engineering, Garching/Munich 2009, ed. by S. Wagner, M. Steinmetz, A. Bode and M. M. Müller (Springer, Heidelberg, 2010), pp. 599612.
[arXiv:0910.5126]
We present the results of numerical studies for selected
materials with strongly correlated electrons using a
combination of the localdensity approximation and dynamical
meanfield theory (DMFT). For the solution of the DMFT
equations a continuoustime quantum MonteCarlo algorithm
was employed. All simulations were performed on the
supercomputer HLRB II at the Leibniz Rechenzentrum in
Munich. Specifically we have analyzed the pressure induced
metalinsulator transitions in Fe_{2}O_{3}
and NiS_{2}, the charge susceptibility of the
fluctuatingvalence elemental metal Yb, and the spectral
properties of a covalent bandinsulator model which includes
local electronic correlations.

M. Eckstein, A. Hackl, S. Kehrein, M. Kollar, M. Moeckel, P. Werner, and F. A. Wolf,
New theoretical approaches for correlated systems in nonequilibrium,
Eur. Phys. J. Special Topics 180, 217 (2010).
Volume on Cooperative Phenomena in Solids with Electronic Correlations [Editorial].
[arXiv:1005.5097]
We review recent developments in the theory of interacting
quantum manyparticle systems that are not in
equilibrium. We focus mainly on the nonequilibrium
generalizations of the flow equation approach and of
dynamical meanfield theory (DMFT). In the nonequilibrium
flow equation approach one first diagonalizes the
Hamiltonian iteratively, performs the time evolution in this
diagonal basis, and then transforms back to the original
basis, thereby avoiding a direct perturbation expansion with
errors that grow linearly in time. In nonequilibrium DMFT,
on the other hand, the Hubbard model can be mapped onto a
timedependent selfconsistent singlesite problem. We
discuss results from the flow equation approach for
nonlinear transport in the Kondo model, and further
applications of this method to the relaxation behavior in
the ferromagnetic Kondo model and the Hubbard model after an
interaction quench. For the interaction quench in the
Hubbard model, we have also obtained numerical DMFT results
using quantum Monte Carlo simulations. In agreement with the
flow equation approach they show that for weak coupling the
system relaxes to a "prethermalized" intermediate state
instead of rapid thermalization. We discuss the description
of nonthermal steady states with generalized Gibbs
ensembles.

J. Kuneš, I. Leonov, M. Kollar, K. Byczuk, V. I. Anisimov, and D. Vollhardt,
Dynamical meanfield approach to materials with strong electronic correlations,
Eur. Phys. J. Special Topics 180, 5 (2010).
Volume on Cooperative Phenomena in Solids with Electronic Correlations [Editorial].
[arXiv:1003.3600]
We review recent results on the properties of materials with
correlated electrons obtained within the LDA+DMFT approach,
a combination of a conventional band structure approach
based on the local density approximation (LDA) and the
dynamical meanfield theory (DMFT). The application to four
outstanding problems in this field is discussed: (i) we
compute the full valence band structure of the
chargetransfer insulator NiO by explicitly including the
pd hybridization, (ii) we explain the origin for the
simultaneously occuring metalinsulator transition and
collapse of the magnetic moment in MnO and
Fe_{2}O_{3}, (iii) we describe a novel
GGA+DMFT scheme in terms of planewave pseudopotentials
which allows us to compute the orbital order and cooperative
JahnTeller distortion in KCuF_{3} and LaMnO_{3}, and
(iv) we provide a general explanation for the appearance of
kinks in the effective dispersion of correlated electrons in
systems with a pronounced threepeak spectral function
without having to resort to the coupling of electrons to
bosonic excitations. These results provide a considerable
progress in the fully microscopic investigations of
correlated electron materials.

M. Eckstein and M. Kollar,
Nearadiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy,
New J. Phys.12, 055012 (2010)
[ PDF / IOP+DPG 2010 ].
Focus on Dynamics and Thermalization in Isolated Quantum ManyBody Systems [Editorial].
[arXiv:0911.1282]
We study the excitation energy for slow changes of the
hopping parameter in the FalicovKimball model with
nonequilibrium dynamical meanfield theory. The excitation
energy vanishes algebraically for long ramp times with an
exponent that depends on whether the ramp takes place
within the metallic phase, within the insulating phase, or
across the Mott transition line. For ramps within metallic
or insulating phase the exponents are in agreement with a
perturbative analysis for small ramps. The perturbative
expression quite generally shows that the exponent depends
explicitly on the spectrum of the system in the initial
state and on the smoothness of the ramp protocol. This
explains the qualitatively different behavior of gapless
(e.g., metallic) and gapped (e.g., Mott insulating)
systems. For gapped systems the asymptotic behavior of the
excitation energy depends only on the ramp protocol and
its decay becomes faster for smoother ramps. For gapless
systems and sufficiently smooth ramps the asymptotics are
rampindependent and depend only on the intrinsic spectrum
of the system. However, the intrinsic behavior is
unobservable if the ramp is not smooth enough. This is
relevant for ramps to small interaction in the fermionic
Hubbard model, where the intrinsic cubic falloff of the
excitation energy cannot be observed for a linear ramp due
to its kinks at the beginning and the end.

M. Eckstein, M. Kollar, and P. Werner,
Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity,
Phys. Rev. B 81, 115131 (2010)
[ PDF / AIP 2010 ].
[arXiv:0910.5674]
We use nonequilibrium dynamical meanfield theory in
combination with a recently developed Quantum Monte Carlo
impurity solver to study the realtime dynamics of a Hubbard
model which is driven out of equilibrium by a sudden
increase in the onsite repulsion U. We discuss the
implementation of the selfconsistency procedure and some
important technical improvements of the QMC method. The
exact numerical solution is compared to iterated
perturbation theory, which is found to produce accurate
results only for weak interaction or short
times. Furthermore we calculate the spectral functions and
the optical conductivity from a Fourier transform on the
finite Keldysh contour, for which the numerically accessible
timescales allow to resolve the formation of Hubbard bands
and a gap in the strongly interacting regime. The spectral
function, and all oneparticle quantities that can be
calculated from it, thermalize rapidly at the transition
between qualitatively different weak and strongcoupling
relaxation regimes.

M. Eckstein, M. Kollar, and P. Werner,
Thermalization after an interaction quench in the Hubbard model,
Phys. Rev. Lett. 103, 056403 (2009)
[ PDF / AIP 2009 ].
Selected for vjaqf.org:
Virtual Journal of Atomic Quantum Fluids 1/2 (2009).
[arXiv:0904.0976]
We use nonequilibrium dynamical meanfield theory to study
the time evolution of the fermionic Hubbard model after an
interaction quench. Both in the weakcoupling and in the
strongcoupling regime the system is trapped in
quasistationary states on intermediate time scales. These
two regimes are separated by a sharp crossover at
U_{c}^{dyn}=0.8 in units of the bandwidth,
where fast thermalization occurs. Our results indicate a
dynamical phase transition which should be observable in
experiments on trapped fermionic atoms.

M. Eckstein and M. Kollar,
Measuring correlated electron dynamics with timeresolved photoemission spectroscopy,
Phys. Rev. B 78, 245113 (2008)
[ PDF / AIP 2008 ].
[arXiv:0809.4282]
Timeresolved photoemission experiments can reveal
fascinating quantum dynamics of correlated electrons.
However, the thermalization of the electronic system is
typically so fast that very short probe pulses are necessary
to resolve the time evolution of the quantum state, and this
leads to poor energy resolution due to the energytime
uncertainty relation. Although the photoemission intensity
can be calculated from the nonequilibrium electronic Green
functions, the converse procedure is therefore difficult.
We analyze a hypothetical timeresolved photoemission
experiment on a correlated electronic system, described by
the FalicovKimball model in dynamical meanfield theory,
which relaxes between metallic and insulating phases. We
find that the realtime Green function which describes the
transient behavior during the buildup of the metallic state
cannot be determined directly from the photoemission
signal. On the other hand, the characteristic
collapseandrevival oscillations of an excited Mott
insulator can be observed as oscillating weight in the
center of the Mott gap in the timedependent photoemission
spectrum.

M. Eckstein and M. Kollar,
Theory of timeresolved optical spectroscopy on correlated electron systems,
Phys. Rev. B 78, 205119 (2008)
[ PDF / AIP 2008 ].
Selected for PRB Editors' Suggestions.
Selected for vjultrafast.org:
Virtual Journal of Ultrafast Science 7/12 (2008).
[arXiv:0808.1005]
The realtime dynamics of interacting electrons out of equilibrium
contains detailed microscopic information about electronically
correlated materials, which can be read out with timeresolved optical
spectroscopy. The reflectivity that is typically measured in
pumpprobe experiments is related to the nonequilibrium optical
conductivity. We show how to express this quantity in terms of
realtime Green functions using dynamical meanfield theory. As an
application we study the electrical response of the FalicovKimball
model during the ultrafast buildup of the gapped phase at large
interaction.

M. Kollar and M. Eckstein,
Relaxation of a onedimensional Mott insulator after an interaction quench,
Phys. Rev. A 78, 013626 (2008)
[ PDF / AIP 2008 ].
[arXiv:0804.2254]
We obtain the exact time evolution for the onedimensional
integrable fermionic 1/r Hubbard model after a sudden change
of its interaction parameter, starting from either a metallic
or a Mottinsulating eigenstate. In all cases the system
relaxes to a new steady state, showing that the presence of
the Mott gap does not inhibit relaxation. The properties of
the final state are described by a generalized Gibbs ensemble.
We discuss under which conditions such ensembles provide the
correct statistical description of isolated integrable systems
in general. We find that generalized Gibbs ensembles do
predict the properties of the steady state correctly, provided
that the observables or initial states are sufficiently
uncorrelated in terms of the constants of motion.

M. Eckstein and M. Kollar,
Nonthermal steady states after an interaction quench in the FalicovKimball model,
Phys. Rev. Lett. 100, 120404 (2008)
[ PDF / AIP 2008 ].
[arXiv:0707.2789]
We present the exact solution of the FalicovKimball model
after a sudden change of its interaction parameter using
dynamical meanfield theory. For different interaction
quenches between the homogeneous metallic and insulating
phases the system relaxes to a nonthermal steady state on
time scales on the order of hbar/bandwidth, showing collapse
and revival with an approximate period of h/interaction if the
interaction is large. We discuss the reasons for this behavior
and provide a statistical description of the final steady
state by means of generalized Gibbs ensembles.

L. Zherlitsyna, N. Auner, M. Bolte, Y. Pozdniakova, O. Shchegolikhina,
K. Lyssenko, V. Pashchenko, B. Wolf, M. Lang, F. Schütz,
M. Kollar, F. Sauli, and P. Kopietz,
Synthesis, Structure and Magnetic Properties of a Novel Hexanuclear Copper Methylsiloxane Complex,
Eur. J. Inorg. Chem. 30, 4827 (2007).
A new hexanuclear copper(II) sandwich complex based on two
12membered macrocyclic methylsiloxanolate ligands,
Cu_{6}[(MeSiO_{2})_{6}]_{2}·6DMF,
was synthesized and characterized by single crystal Xray
diffraction analysis and magnetic measurements. The cluster
compound crystallizes in the monoclinic system, space group
P21/n (No.14), with a=13.3728(5)Å,
b=15.4281(7)Å, c=17.4335(7)Å,
β=98.932(3)° and Z=2. The unit cell contains two
identical macromolecules, each consisting of six interacting
Cu^{2+} (S=1/2) ions. Within the macromolecule the
six oxygenbridged Cu^{2+} ions are arranged into an
almost regular hexagon. An analysis of the hightemperature
part of the magnetic susceptibility reveals that the complex
has a strong average ferromagnetic CuCu exchange
interaction of J_{av}/k_{B}=50.4±1K
with a highspin S=3 ground state. A satisfactory fit for
the magnetic susceptibility and the magnetization in the
whole accessible temperature range is obtained from a
Heisenberg model with nonuniform exchange couplings within a
ring, corresponding to a system of two weakly coupled
trimers with a ferromagnetic intratrimer exchange coupling
of J/k_{B}=72.5 K and a ferromagnetic intertrimer
exchange coupling of J'/k_{B}=7K.

M. Sentef, M. Kollar, and A. P. Kampf,
Spin transport in Heisenberg antiferromagnets in two and three dimensions,
Phys. Rev. B 75, 214403 (2007)
[ PDF / AIP 2007 ].
Selected for vjnano.org:
Virtual Journal of Nanoscale Science & Technology 15/24 (2007).
[condmat/0612215]
We analyze spin transport in insulating antiferromagnets
described by the XXZ Heisenberg model in two and three
dimensions. Spin currents can be generated by a
magneticfield gradient or, in systems with spinorbit
coupling, perpendicular to a timedependent electric
field. The Kubo formula for the longitudinal spin
conductivity is derived analogously to the Kubo formula for
the optical conductivity of electronic systems. The spin
conductivity is calculated within interacting spinwave
theory. In the Ising regime, the XXZ magnet is a spin
insulator. For the isotropic Heisenberg model, the
dimensionality of the system plays a crucial role: In d=3
the regular part of the spin conductivity vanishes linearly
in the zero frequency limit, whereas in d=2 it approaches a
finite zero frequency value.

K. Byczuk, W. Hofstetter, M. Kollar, and D. Vollhardt,
Surprises in Correlated Electron Physics,
Acta Phys. Pol. A 111, 549 (2007).
Strong electronic correlations and especially the interplay
between correlations and disorder lead to many interesting
and quite unexpected phenomena. A short summary of our
recent investigations into the properties of strongly
correlated electron systems with and without disorder using
the dynamical meanfield theory is presented.

M. Eckstein, M. Kollar, and D. Vollhardt,
Isosbestic points in the spectral function of correlated electrons,
J. Low Temp. Phys.147, 279 (2007).
[condmat/0609464]
We investigate the properties of the spectral function
A(&omega,U) of correlated electrons within the Hubbard model
and dynamical meanfield theory. Curves of A(&omega,U)
vs. &omega for different values of the interaction U are
found to intersect near the bandedges of the
noninteracting system. For a wide range of U the crossing
points are located within a sharply confined region. The
precise location of these 'isosbestic points' depends on
details of the noninteracting band structure. Isosbestic
points of dynamic quantities therefore provide valuable
insights into microscopic energy scales of correlated
systems.

M. Eckstein, M. Kollar, M. Potthoff, and D. Vollhardt,
Phase separation in the particlehole asymmetric Hubbard model,
Phys. Rev. B 75, 125103 (2007)
[ PDF / AIP 2007 ].
[condmat/0610803]
The paramagnetic phase diagram of the Hubbard model with
nearestneighbor (NN) and nextnearestneighbor (NNN)
hopping on the Bethe lattice is computed at halffilling and
in the weakly doped regime using the selfenergy functional
approach for dynamical meanfield theory. NNN hopping breaks
the particlehole symmetry and leads to a strong asymmetry
of the electrondoped and holedoped regimes. Phase
separation occurs at and near halffilling, and the critical
temperature of the Mott transition is strongly
suppressed.

K. Byczuk, M. Kollar, K. Held, Y.F. Yang, I. A. Nekrasov, Th. Pruschke, and D. Vollhardt,
Kinks in the dispersion of strongly correlated electrons,
Nature Physics 3, 168 (2007) + supplementary information
[ PDF / accepted manuscript ]
Advance online publication, 18 Feb 2007.
Discussed in News and Views.
Selected for condmatjournalclub.org: Journal Club for Condensed Matter Physics, 29 Oct 2007 [ PDF ].
[condmat/0609594]
The properties of condensed matter are determined by
singleparticle and collective excitations and their
interactions. These quantummechanical excitations are
characterized by an energy E and a momentum \hbar k which
are related through their dispersion E_k. The coupling of
two excitations may lead to abrupt changes (kinks) in the
slope of the dispersion. Such kinks thus carry important
information about interactions in a manybody system. For
example, kinks detected at 4070 meV below the Fermi level
in the electronic dispersion of hightemperature
superconductors are taken as evidence for phonon or
spinfluctuation based pairing mechanisms. Kinks in the
electronic dispersion at binding energies ranging from 30 to
800 meV are also found in various other metals posing
questions about their origins. Here we report a novel,
purely electronic mechanism yielding kinks in the electron
dispersions. It applies to strongly correlated metals whose
spectral function shows well separated Hubbard subbands and
central peak as, for example, in transition
metaloxides. The position of the kinks and the energy range
of validity of Fermiliquid (FL) theory is determined solely
by the FL renormalization factor and the bare, uncorrelated
band structure. Angleresolved photoemission spectroscopy
(ARPES) experiments at binding energies outside the FL
regime can thus provide new, previously unexpected
information about strongly correlated electronic systems.

V. Pashchenko, M. Lang, B. Wolf, L. Zherlitsyna, N. Auner, O. Shchegolikhina, Yu. Pozdniakova, F. Schütz, P. Kopietz, and M. Kollar,
Structural and magnetic investigations on new molecular quantum rings,
Comptes Rendus Chimie 10, 89 (2007).
We report on a comparative investigation of the structural
and magnetic properties of three oxygenbridged polynuclear
(N = 6, 8, 10) Cu(II) cyclomethylsiloxanolate complexes,
Cu_{6}[(MeSiO_{2})_{6}]_{2}·6DMF,
{Cu_{8}[(MeSiO_{2})_{8}]_{2}·8DMF}·EtOH
and
{Cu_{10}[(MeSiO_{2})_{10}]_{2}·10DMF}·6DMF. All
three molecular complexes have a planar ringshaped
configuration of the copper S = 1/2 spins. The analysis of
the magnetic data, with particular emphasis placed on the
hightemperature behaviour, together with the structural
information enables us to correlate the evolution of the
exchange coupling J between the magnetic S = 1/2 centers of
the quantum ring as a function of the number N of magnetic
sites to the structural changes of the molecular crystals.

X. Ren, I. Leonov, G. Keller, M. Kollar, I. Nekrasov, and D. Vollhardt,
LDA+DMFT computation of the electronic spectrum of NiO,
Phys. Rev. B 74, 195114 (2006)
[ PDF / AIP 2006 ].
[condmat/0606285]
The electronic spectrum, energy gap and local magnetic
moment of paramagnetic NiO are computed using the local
density approximation plus dynamical meanfield theory
(LDA+DMFT). To this end the noninteracting Hamiltonian
obtained within the LDA is expressed in Wannier function
basis, with only the five antibonding bands with mainly Ni
3d character taken into account. Complementing it by local
Coulomb interactions one arrives at a materialspecific
manybody Hamiltonian which is solved by DMFT together with
quantum Monte Carlo (QMC) simulations. The large insulating
gap in NiO is found to be a result of the strong electronic
correlations in the paramagnetic state. In the vicinity of
the gap region, the shape of the electronic spectrum
calculated in this way is in good agreement with the
experimental xrayphotoemission and
bremsstrahlungisochromatspectroscopy results of Sawatzky
and Allen. The value of the local magnetic moment computed
in the paramagnetic phase (PM) agrees well with that
measured in the antiferromagnetic (AFM) phase. Our results
for the electronic spectrum and the local magnetic moment in
the PM phase are in accordance with the experimental finding
that AFM longrange order has no significant influence on
the electronic structure of NiO.

I. A. Nekrasov, K. Held, G. Keller,
D. E. Kondakov, Th. Pruschke, M. Kollar,
O. K. Andersen, V. I. Anisimov, and
D. Vollhardt,
Momentumresolved spectral functions of SrVO_{3} calculated by LDA+DMFT,
Phys. Rev. B 73, 155112 (2006)
[PDF / AIP 2006 ].
[condmat/0508313]
LDA+DMFT, the merger of density functional theory in the
local density approximation and dynamical meanfield theory,
has been mostly employed to calculate kintegrated
spectra accessible by photoemission spectroscopy. In this
paper, we calculate kresolved spectral functions by
LDA+DMFT. To this end, we employ the Nth order muffintin
(NMTO) downfolding to set up an effective lowenergy
Hamiltonian with three t_{2g} orbitals. This
downfolded Hamiltonian is solved by DMFT yielding
kdependent spectra. Our results show a renormalized
quasiparticle band over a broad energy range from
0.7 eV to +0.9 eV with small "kinks" discernible
in the dispersion below the Fermi energy.

G. Keller, K. Held, V. Eyert, V. I. Anisimov, K. Byczuk, M. Kollar, I. Leonov, X. Ren, and D. Vollhardt,
Realistic Modeling of Materials with Strongly Correlated Electrons,
in: NIC Symposium 2006, ed. by G. Münster, D. Wolf, and M. Kremer, NIC Series, Vol. 32, pp. 183190 (NIC Scientific Council, 2006) [PDF at fzjuelich.de].

V. Pashchenko, B. Brendel, B. Wolf, M. Lang, K. Lyssenko, O. Shchegolikhina, Y. Molodtsova, L. Zherlitsyna, N. Auner, F. Schütz, M. Kollar, P. Kopietz, and N. Harrison,
Synthesis, structure and magnetic properties of a novel linear Cu(II)trimer complex,
Eur. J. Inorg. Chem. 2005, 4617 (2005).
A new hexanuclear copper(II) sandwich complex based on two
10membered macrocyclic phenylsiloxanolate ligands,
{Cu_{6}[(C_{6}H_{5}SiO_{2})_{5}]_{2}(OH)_{2}(C_{10}0H_{8}N_{2})_{2}}·4(DMF)·3(H_{2}O),
was synthesized and characterized by singlecrystal Xray
diffraction and measurements of the magnetic susceptibility
and isothermal magnetization. The cluster compound
crystallizes in the triclinic system, space group P (No. 2),
with a = 14.925(3) Å,
b = 16.745(2) Å,
c = 23.053(3) Å,
α = 83.079(9)°, β =
84.836(13)°, γ = 65.019(17)°, and
Z = 2. The unit cell contains two identical
molecules, each consisting of six interacting
Cu^{2+} (S = 1/2) ions. Within the
molecule, the six Cu^{2+} ions are arranged in two
almost linear, parallel trimers. While pairs of oxygen atoms
link the Cu^{2+} ions within the trimers, single
oxygen atoms residing at the ends of the trimers provide the
strongest intertrimer bonds. Magnetic measurements reveal an
antiferromagnetic intratrimer exchange interaction,
J/kB = 85 K, as the dominant magnetic
coupling of the complex. By introducing a weak
antiferromagnetic intertrimer coupling,
J/kB = 3.5 K, a satisfactory description of
the magnetic behavior over a wide range of temperature and
magnetic field is obtained. The departure of the model
curves from the data at the lowest available temperature
indicates the presence of additional, weak intra and/or
intermolecular interactions.

M. Kollar, M. Eckstein, K. Byczuk, N. Blümer, P. van Dongen, M. H. Radke de Cuba, W. Metzner, D. Tanaskovic, V. Dobrosavljevic, G. Kotliar, and D. Vollhardt,
Green functions for nearest and nextnearestneighbor hopping on the Bethe lattice,
Ann. Phys. (Leipzig) 14, 642 (2005).
[condmat/0504637]
We calculate the local Green function for a
quantummechanical particle with hopping between nearest and
nextnearest neighbors on the Bethe lattice, where the
onsite energies may alternate on sublattices. For infinite
connectivity the renormalized perturbation expansion is
carried out by counting all nonselfintersecting paths,
leading to an implicit equation for the local Green
function. By integrating out branches of the Bethe lattice
the same equation is obtained from a path integral approach
for the partition function. This also provides the local
Green function for finite connectivity. Finally, a recently
developed topological approach is extended to derive an
operator identity which maps the problem onto the case of
only nearestneighbor hopping. We find in particular that
hopping between nextnearest neighbors leads to an
asymmetric spectrum with additional vanHove singularities.

M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt,
Hopping on the Bethe lattice: Exact results for densities of states and dynamical meanfield theory,
Phys. Rev. B 71, 235119 (2005)
[ PDF / AIP 2005 ].
[condmat/0409730]
We derive an operator identity which relates tightbinding
Hamiltonians with arbitrary hopping on the Bethe lattice to
the Hamiltonian with nearestneighbor hopping. This provides
an exact expression for the density of states (DOS) of a
noninteracting quantummechanical particle for any
hopping. We present analytic results for the DOS
corresponding to hopping between nearest and nextnearest
neighbors, and also for exponentially decreasing hopping
amplitudes. Conversely it is possible to construct a hopping
Hamiltonian on the Bethe lattice for any given DOS. These
methods are based only on the socalled distance regularity
of the infinite Bethe lattice, and not on the absence of
loops. Results are also obtained for the triangular Husimi
cactus, a recursive lattice with loops. Furthermore we
derive the exact selfconsistency equations arising in the
context of dynamical meanfield theory, which serve as a
starting point for studies of Hubbardtype models with
frustration.

F. Schütz, P. Kopietz, and M. Kollar,
What are spin currents in Heisenberg magnets?
Eur. J. Phys. B 41, 557 (2004).
[condmat/0405312]
We discuss the proper definition of the spin current
operator in Heisenberg magnets subject to inhomogeneous
magnetic fields. We argue that only the component of the
naive "current operator" J_{i}j S_{i} x
S_{j} in the plane spanned by the local order
parameters <S_{i}> and <S_{j}>
is related to real transport of magnetization. Within a mean
field approximation or in the classical ground state the
spin current therefore vanishes. Thus, finite spin currents
are a direct manifestation of quantum correlations in the
system.

V. Pashchenko, B. Brendel, B. Wolf, M. Lang, M. Kollar, F. Schütz, P. Kopietz, Y. Molodtsova, O. Shchegolikhina, N. Auner, and J. Bats,
Structural and magnetic investigations on a new molecular quantum magnet,
J. Mag. Magn. Mat. 272276, e755 (2004).
We report structural and magnetic investigations on a new
hexacopper (II) siloxanolate cluster compound
[C_{92}H_{102}Cu_{6}N_{8}O_{29}Si_{10}]. The
system, crystallizing in the triclinic space group
P^{_}1 (No. 2), has two identical
macromolecules per unit cell. Each cluster contains six
interacting Cu^{2+} ions. We find a crossover from a
12spin paramagnetic state at high temperatures to a 4spin
lowtemperature configuration accompanied by the formation
of an S=1 cluster ground state. A minimal magnetic model is
discussed which may account for these observations.

F. Schütz, M. Kollar, and P. Kopietz,
Persistent spin currents in mesoscopic Haldane gap spin rings,
Phys. Rev. B 69, 035313 (2004)
[ PDF / AIP 2004 ].
[condmat/0308230]
Using a modified spinwave approach, we show that in the
presence of an inhomogeneous magnetic field or an in plane
inhomogeneous electric field a mesoscopic antiferromagnetic
Heisenberg ring with integer spin (i.e., a Haldane gap
system) exhibits a persistent circulating spin current. Due
to quantum fluctuations the current has a finite limit on
the order of g mu_{B} c/L at zero temperature,
provided the staggered correlation length xi exceeds the
circumference L of the ring, in close analogy to ballistic
charge currents in mesoscopic normal metal rings. Here c is
the spinwave velocity, g is the gyromagnetic ratio and
mu_{B} is the Bohr magneton. For xi<<L the
current is exponentially suppressed.

F. Schütz, M. Kollar, and P. Kopietz,
Persistent spin currents in mesoscopic Heisenberg rings,
Phys. Rev. Lett. 91, 017205 (2003)
[ PDF / AIP 2003 ].
Selected for vjnano.org:
Virtual Journal of Nanoscale Science & Technology, 8/2 (2003).
[condmat/0301351]
We show that at low temperatures T an inhomogeneous radial
magnetic field with magnitude B gives rise to a persistent
magnetization current around a mesoscopic ferromagnetic
Heisenberg ring. Under optimal conditions this spin current
can be as large as g mu_{B} (T / hbar) exp (  2 pi
(g mu_{B} B / Delta )^{1/2} ), as obtained
from leadingorder spinwave theory. Here g is the
gyromagnetic factor, mu_{B} is the Bohr magneton,
and Delta is the energy gap between the ground state and the
first spinwave excitation. The magnetization current endows
the ring with an electric dipole moment.

M. Kollar, I. Spremo, and P. Kopietz,
Spin wave theory at constant order parameter,
Phys. Rev. B 67, 104427 (2003)
[ PDF / AIP 2003 ].
[condmat/0210578]
We derive the lowtemperature properties of spinS quantum
Heisenberg magnets from the Gibbs free energy G(M) for fixed
order parameter M. Assuming that the lowlying elementary
excitations of the system are renormalized spin waves, we
show that a straightforward 1/S expansion of G(M) yields
qualitatively correct results for the lowtemperature
thermodynamics, even in the absence of longrange magnetic
order. We explicitly calculate the twoloop correction to
the susceptibility of the ferromagnetic Heisenberg chain and
show that it quantitatively modifies the meanfield result.

L. Bartosch, M. Kollar, and P. Kopietz,
Ferromagnetic Luttinger liquids,
Phys. Rev. B 67, 092403 (2003)
[ PDF / AIP 2003 ].
[condmat/0207383]
We study weak itinerant ferromagnetism in onedimensional
Fermi systems using perturbation theory and bosonization. We
find that longitudinal spin fluctuations propagate
ballistically with velocity v_{m} <<
v_{F}, where v_{F} is the Fermi
velocity. This leads to a large anomalous dimension in the
spinchannel and strong algebraic singularities in the
singleparticle spectral function and in the transverse
structure factor for momentum transfers q ~ 2
Delta/v_{F}, where 2 Delta is the exchange
splitting.

M. Kollar,
Construction of a dispersion relation from an arbitrary density of states,
Int. J. Mod. Phys. B 16, 3491 (2002).
[condmat/0105068]
The dispersion relations of energy bands in solids are
characterized by their density of states, but a given
density of states may originate from various band
structures. We show how a spherically symmetric dispersion
can be constructed for any oneband density of states. This
method is applied to one, two and threedimensional
systems. It also serves to establish that any oneband
spectrum with finite bandwidth can be obtained from a
properly scaled dispersion relation in the limit of infinite
dimensions.

M. Kollar and D. Vollhardt,
Exact analytic results for the Gutzwiller wave function with finite magnetization,
Phys. Rev. B 65, 155121 (2002)
[ PDF / AIP 2002 ].
[condmat/0111043]
We present analytic results for groundstate properties of
Hubbardtype models in terms of the Gutzwiller variational
wave function with nonzero values of the magnetization
m. In dimension D=1 approximationfree evaluations are made
possible by appropriate canonical transformations and an
analysis of Umklapp processes. We calculate the double
occupation and the momentum distribution, as well as its
discontinuity at the Fermi surface, for arbitrary values of
the interaction parameter g, density n, and magnetization
m. These quantities determine the expectation value of the
onedimensional Hubbard Hamiltonian for any symmetric,
monotonically increasing dispersion epsilon_{k}. In
particular for nearestneighbor hopping and densities away
from half filling the Gutzwiller wave function is found to
predict ferromagnetic behavior for sufficiently large
interaction U.

M. Kollar and S. Sachdev,
Tunneling gap of two laterally separated quantum Hall systems,
Phys. Rev. B 65, R121304 (2002)
[ PDF / AIP 2002 ].
[condmat/0106001]
We use a method of matched asymptotics to determine the
energy gap of two counterpropagating, strongly interacting,
quantum Hall edge states. The microscopic edge state
dispersion and Coulomb interactions are used to precisely
constrain the shortdistance behavior of an integrable field
theory, which then determines the low energy spectrum. We
discuss the relationship of our results to the tunneling
measurements of Kang et al., Nature 403, 59 (2000).

D. Vollhardt, N. Blümer, K. Held, and M. Kollar,
Metallic ferromagnetism  an electronic correlation phenomenon,
in: BandFerromagnetism: GroundState and FiniteTemperature Phenomena,
edited by K. Baberschke, M. Donath, and W. Nolting,
Lecture Notes in Physics, Vol. 580 (Springer, Heidelberg, 2001), pp. 191207.
[condmat/0012203]
New insights into the microscopic origin of itinerant
ferromagnetism were recently gained from investigations of
electronic lattice models within dynamical meanfield theory
(DMFT). In particular, it is now established that even in
the oneband Hubbard model metallic ferromagnetism is stable
at intermediate values of the interaction U and density n on
regular, frustrated lattices. Furthermore, band degeneracy
along with Hund's rule couplings is very effective in
stabilizing metallic ferromagnetism in a broad range of
electron fillings. DMFT also permits one to investigate more
complicated correlation models, e.g., the ferromagnetic
Kondo lattice model with Coulomb interaction, describing
electrons in manganites with perovskite structure. Here we
review recent results obtained with DMFT which help to
clarify the origin of bandferromagnetism as a correlation
phenomenon.

M. Kollar and D. Vollhardt,
Correlated hopping of electrons: Effect on the BrinkmanRice transition and the stability of metallic ferromagnetism,
Phys. Rev. B 63, 045107 (2001)
[ PDF / AIP 2001 ].
[condmat/0008015]
We study the Hubbard model with bondcharge interaction
(correlated hopping) in terms of the Gutzwiller wave
function. We show how to express the Gutzwiller expectation
value of the bondcharge interaction in terms of the
correlated momentumspace occupation. This relation is valid
in all spatial dimensions. We find that in infinite
dimensions, where the Gutzwiller approximation becomes
exact, the bondcharge interaction lowers the critical
Hubbard interaction for the BrinkmanRice metalinsulator
transition. The bondcharge interaction also favors
ferromagnetic transitions, especially if the density of
states is not symmetric and has a large spectral weight
below the Fermi energy.

M. Kollar and D. Vollhardt,
Thermodynamically consistent equilibrium properties of normalliquid Helium3,
Phys. Rev. B 61, 15347 (2000)
[ PDF / AIP 2000 ];
Erratum: ibid. 72, 139903 (2005)
[ PDF / AIP 2005 ].
Helium3Kalkulator (Java applet).
[condmat/9906222]
The highprecision data for the specific heat
C_{V}(T,V) of normalliquid Helium3 obtained by
Greywall, taken together with the molar volume
V(T_{0},P) at one temperature T_{0}, are
shown to contain the complete thermodynamic information
about this phase in zero magnetic field. This enables us to
calculate the T and P dependence of all equilibrium
properties of normalliquid Helium3 in a thermodynamically
consistent way for a wide range of parameters. The results
for the entropy S(T,P), specific heat at constant pressure
C_{P}(T,P), molar volume V(T,P), compressibility
kappa(T,P), and thermal expansion coefficient alpha(T,P) are
collected in the form of figures and tables. This provides
the first complete set of thermodynamically consistent
values of the equilibrium quantities of normalliquid
Helium3. We find, for example, that alpha(T,P) has a
surprisingly intricate pressure dependence at low
temperatures, and that the curves alpha(T,P) vs T do not
cross at one single temperature for all pressures, in
contrast to the curves presented in the comprehensive survey
of helium by Wilks. Corrected in condmat/9906222v3: The
sign of the coefficient d_{0} was misprinted in
Table I of condmat/9906222v1 and v2. It now correctly reads
d_{0}=7.1613436. All results in the paper were
obtained with the correct value of d_0. (We would like to
thank for E. Collin, H. Godfrin, and Y. Bunkov for finding
this misprint.)

N. Chandra, M. Kollar, and D. Vollhardt,
Nearly universal crossing point of the specific heat curves of Hubbard models,
Phys. Rev. B 59, 10541 (1999)
[ PDF / AIP 1999 ].
[condmat/9810391]
A nearly universal feature of the specific heat curves
C(T,U) vs. T for different U of a general class of Hubbard
models is observed. That is, the value C_{+} of the
specific heat curves at their hightemperature crossing
point T_{+} is almost independent of lattice
structure and spatial dimension d, with
C_{+}/k_{B} approx 0.34. This surprising
feature is explained within second order perturbation theory
in U by identifying two small parameters controlling the
value of C_{+}: the integral over the deviation of
the density of states N(E) from a constant value,
characterized by dN = int N(E)1/2 dE, and the inverse
dimension, 1/d.

D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, M. Ulmke, and J. Wahle,
Metallic ferromagnetism: Progress in our understanding of an old strongcoupling problem,
Advances in Solid State Physics 38, 383 (1999).
[condmat/9804112]
Metallic ferromagnetism is in general an intermediate to
strong coupling phenomenon. Since there do not exist
systematic analytic methods to investigate such types of
problems, the microscopic origin of metallic ferromagnetism
is still not sufficiently understood. However, during the
last two or three years remarkable progress was made in this
field: It is now certain that even in the oneband Hubbard
model metallic ferromagnetism is stable in dimensions d=1,
2, and infinity on regular lattices and at intermediate
values of the interaction U and density n. In this paper the
basic questions and recent insights regarding the
microscopic conditions favoring metallic ferromagnetism in
this model are reviewed. These findings are contrasted with
the results for the orbitally degenerate case.

M. Kollar,
Magnetische und thermodynamische
Eigenschaften korrelierter Fermionensysteme, ISBN389639150X
(WißnerVerlag,
Augsburg, 1998), Dissertation.

D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, and M. Ulmke,
Nonperturbative approaches to magnetism in strongly correlated electron systems,
Z. Phys. B 103, 283 (1997).
[condmat/9701150]
The microscopic basis for the stability of itinerant
ferromagnetism in correlated electron systems is
examined. To this end several routes to ferromagnetism are
explored, using both rigorous methods valid in arbitrary
spatial dimensions, as well as Quantum Monte Carlo
investigations in the limit of infinite dimensions
(dynamical meanfield theory). In particular we discuss the
qualitative and quantitative importance of (i) the direct
Heisenberg exchange coupling, (ii) band degeneracy plus
Hund's rule coupling, and (iii) a high spectral density near
the band edges caused by an appropriate lattice structure
and/or kinetic energy of the electrons. We furnish evidence
of the stability of itinerant ferromagnetism in the pure
Hubbard model for appropriate lattices at electronic
densities not too close to halffilling and large enough
U. Already a weak direct exchange interaction, as well as
band degeneracy, is found to reduce the critical value of U
above which ferromagnetism becomes stable
considerably. Using similar numerical techniques the Hubbard
model with an easy axis is studied to explain metamagnetism
in strongly anisotropic antiferromagnets from a unifying
microscopic point of view.

M. Kollar, R. Strack, and D. Vollhardt,
Ferromagnetism in correlated electron systems: Generalization of Nagaoka's theorem,
Phys. Rev. B 53, 9225 (1996)
[ PDF / AIP 1996 ];
erratum: ibid. 55, E11878 (1997)
[ PDF / AIP 1997 ].
[condmat/9511060]
Nagaoka's theorem on ferromagnetism in the Hubbard model
with one electron less than half filling is generalized to
the case where all possible nearestneighbor Coulomb
interactions (the densitydensity interaction V, bondcharge
interaction X, exchange interaction F, and hopping of double
occupancies F') are included. It is shown that for
ferromagnetic exchange coupling (F>0) ground states with
maximum spin are stable already at finite Hubbard
interaction U>U_{c}. For nonbipartite lattices this
requires a hopping amplitude t<=0. For vanishing F one
obtains U_{c}=infinity as in Nagaoka's theorem. This
shows that the exchange interaction F is important for
stabilizing ferromagnetism at finite U. Only in the special
case X=t the ferromagnetic state is stable even for F=0,
provided the lattice allows the hole to move around loops.
I don't want to achieve immortality through my work; I want to achieve immortality through not dying.
 Woody Allen
