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International Journal of Modern Physics C

Dc conductivity of two-dimensional ionic Hubbard model extracted by analytic continuation

Yiqun Huang, Wanpeng Han, Junsong Sun, Huaiming Guo, Shiping Feng

Published Dec 27, 2023• 0 citations
Publisher

Abstract

The ionic Hubbard model in a two-dimensional square lattice is revisited using determinant quantum Monte Carlo (DQMC) and numerical analytic continuation. From the dc conductivity extracted by stochastic maximum entropy of the DQMC data, we find that the band insulator induced by a staggered potential [Formula: see text] goes through a metallic phase before entering a Mott insulator as the on-site Hubbard interaction U is increased. Moreover, we map out the phase diagram in the [Formula: see text] plane, and reveal a smaller metallic region than that found in the previous studies. Our results provide a more exact location of the phase boundaries, and are an important complement to those obtained by an approximate approach.

DOI
10.1142/s0129183124501031

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The ionic Hubbard model in a two-dimensional square lattice is revisited using determinant quantum Monte Carlo (DQMC) and numerical analytic continuation. From the dc conductivity extracted by stochastic maximum entropy of the DQMC data, we find that the band insulator induced by a staggered potential [Formula: see text] goes through a metallic phase before entering a Mott insulator as the on-site Hubbard interaction U is increased. Moreover, we map out the phase diagram in the [Formula: see text] plane, and reveal a smaller metallic region than that found in the previous studies. Our results provide a more exact location of the phase boundaries, and are an important complement to those obtained by an approximate approach.
The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction UUU, while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization VVV and two types of intralayer staggered potentials $\mathrm{\ensuremath{\Delta}}$: one with the same (in-phase) and the other with a $\ensuremath{\pi}$-phase shift (antiphase) potential between layers. Our determinant quantum Monte Carlo (DQMC) simulations at lowest accessible temperatures demonstrate that the interaction-driven metallic phase between Mott and band insulators expands in the $\mathrm{\ensuremath{\Delta}}\text{\ensuremath{-}}V$ phase diagram of bilayer IHM only for in-phase ionic potentials; while antiphase potential always induces an insulator with charge density order. This implies possible further extension of the ionic Hubbard model from the bilayer case here to a realistic three-dimensional 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 $ Δ$. 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 $ Δ$ 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 $ Δ=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.
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo. At half-filling, when the interaction strength or the staggered potential dominates, we find Mott and band insulators, respectively. When these two energies are of the same order, we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
The interaction-driven insulator-to-metal transition has been reported in the ionic Hubbard model (IHM) for moderate interaction UUU, while its metallic phase only occupies a narrow region in the phase diagram. To explore the enlargement of the metallic regime, we extend the ionic Hubbard model to two coupled layers and study the interplay of interlayer hybridization VVV and two types of intralayer staggered potentials ΔΔΔ: one with the same (in-phase) and the other with a πππ-phase shift (anti-phase) potential between layers. Our determinant Quantum Monte Carlo (DQMC) simulations at lowest accessible temperatures demonstrate that the interaction-driven metallic phase between Mott and band insulators expands in the Δ−VΔ-VΔ−V phase diagram of bilayer IHM only for in-phase ionic potentials; while anti-phase potential always induces an insulator with charge density order. This implies possible further extension of the ionic Hubbard model from the bilayer case here to realistic three-dimensional model.
Quantum Monte Carlo methods are used to study a quantum phase transition in a one-dimensional Hubbard model with on-site interaction U and a staggered ionic potential $(\ensuremath{\Delta}).$ Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wave function and compared to results of previous work using exact diagonalization and Hartree-Fock. We find a transition from a symmetric band insulator to a broken-symmetry bond ordered (BO) phase as the ratio of $U/\ensuremath{\Delta}$ is increased, with a metallic point at the transition. Since it is known that at $\ensuremath{\Delta}=0$ the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed $\ensuremath{\Delta}$ and (ii) decreasing $\ensuremath{\Delta}$ at fixed U. We find no transition from the BO to MI state, and we propose that the symmetric MI state exists only at $\ensuremath{\Delta}\ensuremath{\equiv}0.$