Classical Analogue of the Ionic Hubbard Model

TL;DR

This paper analytically solves the classical analogue of the ionic Hubbard model in one dimension, revealing two insulating phases separated by a metallic phase and confirming findings with Monte Carlo simulations.

Contribution

It introduces an analytical solution for the classical ionic Hubbard model at finite temperature using the transfer matrix method, extending previous quantum-based approaches.

Findings

Identifies two insulating phases at large and small U

Discovers a gapless metallic phase between insulators

Supports results with Monte Carlo simulations

Abstract

In our earlier work [M. Hafez, {\em et al.}, Phys. Lett. A {\bf 373} (2009) 4479] we employed the flow equation method to obtain a classic effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard model (IHM). The classical ionic Hubbard model (CIHM) obtained in this way contains solely Fermionic occupation numbers of two species corresponding to particles with $\up$ and $\down$ spin, respectively. In this paper, we employ the transfer matrix method to analytically solve the CIHM at finite temperature in one dimension. In the limit of zero temperature, we find two insulating phases at large and small Coulomb interaction strength, $U$, mediated with a gap-less metallic phase, resulting in two continuous metal-insulator transitions. Our results are further supported with Monte Carlo simulations.