Mott-Hubbard metal-insulator transition

⁽¹⁾, J. Schlipf

⁽¹⁾, P. G. J. van Dongen

⁽¹⁾, N. Blümer

⁽¹⁾, M. Jarrell

⁽²⁾, S. Kehrein

⁽³⁾, and Th. Pruschke

⁽⁴⁾

⁽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 V₂O₃ 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=bandwidth).

[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).