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

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.