Quantum Monte Carlo Simulation of the two-dimensional ionic Hubbard model

TL;DR

This study uses Quantum Monte Carlo simulations to explore the phase transitions of the two-dimensional ionic Hubbard model, revealing complex behavior including metallic, Mott insulator, and band insulator phases with hysteresis effects.

Contribution

First detailed Quantum Monte Carlo analysis of the 2D ionic Hubbard model showing phase transitions and hysteresis phenomena at low temperature.

Findings

Identification of metallic, Mott insulator, and band insulator phases.

Observation of hysteresis in the metal-Mott insulator transition.

Phase diagram illustrating the different phases at low temperature.

Abstract

The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ \Delta $. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ \Delta $ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ \Delta =0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.