$(1)$Institut für Physik, Universität Augsburg,
D-86135 Augsburg, Germany

$(2)$Department of Physics, University of Cincinnati,
Cincinnati, Ohio 45221, USA

$(3)$Physics Department, Harvard University, Cambridge,
MA 02138, USA

$(4)$Universität Regensburg, 93040 Regensburg, Germany

The explanation of the nature of the Mott-Hubbard metal-insulator
transition, i.e., the transition between a paramagnetic metal and
a paramagnetic insulator driven by electronic interactions, is one
of the classic and fundamental problems in condensed matter
physics [1]. Metal-insulator transitions of this type are, for
example, found in transition metal oxides with partially filled
bands near the Fermi level. For such systems band theory typically
predicts metallic behavior. The most famous example is
V$$_{2}O$$_{3} doped with Cr. A proper understanding of this
phenomenon is made difficult by the fact that one is here dealing
with an *intermediate* coupling problem whose investigation
requires non-perturbative techniques. Recently there have been
some very interesting new developments in this field due to the
application of the dynamical mean-field theory (DMFT) for the
infinite-dimensional Hubbard model [2].

In my talk I will start with a non-technical introduction to the
problem, sketching the historical steps taken in the last 60
years. Then I will present recent results obtained by us using
high-precision quantum Monte Carlo (QMC) simulations to solve the
self-consistency equations of the DMFT [3]. In particular, we
studied the quasiparticle renormalization factor $Z=m/m$
and the compressibility $kappa$ at various temperatures. The
Mott-Hubbard transition is located at the interaction strength
$U$_{c} where $Z(U)$ and $kappa(U)$ turn over sharply, i.e.,
become very small. Then the density of states and the $T$- and
$U$- dependence of the quasiparticle peak and the screened local
moment are discussed. We find that the Fermi-liquid breaks down
*before* the gap opens. From these results we construct the
$T-U$ phase diagram. The transition is shown to be continuous down to at least $T$_{c}=W/140 (W=

[1] N. F. Mott, *Metal-Insulator Transitions*
(Taylor & Francis, London, 1990); F. Gebhard, *The Mott Metal-Insulator Transition* (Springer, Berlin, 1997).

[2] A. Georges, G. Kotliar, W. Krauth and M.J. Rozenberg, Rev. Mod. Phys. **68**, 13 (1996).

[3] J. Schlipf, M. Jarrell, P.G.J. van Dongen, N. Blümer, S.
Kehrein, Th. Pruschke, and D. Vollhardt, Phys. Rev. Lett. **82**, 4890 (1999).