Gutzwiller approximation for paramagnetic ionic Hubbard model: Analytic expression for band-Mott insulator transition

Abstract

The ionic Hubbard model is a paradigmatic setup for studying the competition between band and Mott insulating behavior. Within the variationally exact in infinite dimensions Gutzwiller approximation, we derive a compact analytic expression for the phase boundary between Mott and band insulator. While the method reproduces the expected band-Mott insulator phenomenology, it does not capture the correlated metallic state at finite staggered potential found for example in dynamical mean-field theory. This absence highlights that the metallic phase originates from incoherent Hubbard-band physics rather than Fermi-liquid behavior well captured by Gutzwiller approximation. Our formulation establishes a concise variational framework to ionic Hubbard model, with natural extensions to nonequilibrium setups and spin-exchange dynamics.

Figures (1)

• Figure 1: Phase diagram in the $(\Delta/W, U_c/W)$ plane. The solid line denotes the phase boundary between the Mott insulating and band insulating states, given by $U_c/W = 2\left(1+\sqrt{(\Delta/W)^2+1}\right)$. At $\Delta/W=0$, the system exhibits a correlated metallic phase up to $U_c/W=4$. The region above the boundary corresponds to the Mott insulator, while the region below corresponds to the band insulator. In the inset we provide a schematic phase diagram obtained from dynamical mean-field theory after Ref. Garg_2006.