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Journal of the Korean Physical Society

Quantum Monte Carlo study on an ionic Hubbard model in one dimension

Sung Moon Kim, Ji-Woo Lee

Published Feb 1, 2012• 2 citations
Publisher

Abstract

We study an ionic Hubbard model in one dimension by using a quantum Monte Carlo method. The ionic Hubbard model we study is a strongly correlated model for electrons in alternating potentials with a lattice period of 2. By modifying the Hirsch-Fye algorithm, we incorporate the local variation of the potential in the weight of the partition function at each imaginary-time segment. For a given alternating potential of strength Δ = 1.0, as we change the local Coulomb repulsion, U , between spin-up and spin-down electrons, we calculate various physical quantities, including kinetic energies, correlation energies, and band energies. We try to find the signature of the phase transitions from the behavior of the kinetic energy and that of double occupancies at finite temperatures.

DOI
10.3938/jkps.60.628

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We study an ionic Hubbard model in one dimension by using a quantum Monte Carlo method. The ionic Hubbard model we study is a strongly correlated model for electrons in alternating potentials with a lattice period of 2. By modifying the Hirsch-Fye algorithm, we incorporate the local variation of the potential in the weight of the partition function at each imaginary-time segment. For a given alternating potential of strength Δ = 1.0, as we change the local Coulomb repulsion, U , between spin-up and spin-down electrons, we calculate various physical quantities, including kinetic energies, correlation energies, and band energies. We try to find the signature of the phase transitions from the behavior of the kinetic energy and that of double occupancies at finite temperatures.
We study quantum phase transitions of an ionic Hubbard model in two dimensions. The ionic Hubbard model explains the quantum states of strongly correlated electrons under the influence of checkerboard-type alternating chemical potentials. For a given amplitude of the alternating potentials Δ, we obtain quantum ground states as we tune the local repulsive energy U between a spin-up electron and a spin-down electron by using an exact diagonalization method of a modified Lanczos algorithm. The system undergoes a quantum phase transition from a band insulator to a Mott insulator as U increases at half-filling. We find the signature of a quantum phase transition by investigating the behavior of ground-state energies and that of double occupancies for the size of L × L = 4 × 4, which was the largest possible lattice in this work. We compare our results with those of quantum Monte Carlo simulations employing the Hirsch-Fye algorithm.
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 zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong-coupling phase can only partly be understood in terms of the strong-coupling behavior of the ordinary Hubbard model.
The ionic Hubbard model is investigated at half filling at zero temperature. We apply the cellular dynamical mean-field theory to the one-dimensional ionic Hubbard model to compute local quantities such as double occupancy and staggered charge density. Both quantities provide general transition behavior of the model from a band insulating phase to a Mott insulating phase. The renormalized band gap is introduced as an efficient order parameter for the transition from a band insulator. We also present the spectral properties of the ionic Hubbard model, which exhibit characteristic features for both weak and strong interactions.
Abstract In this work for an interacting electrons system that obeys the Hubbard model, a new quantum Monte Carlo algorithm introduces for calculation of average Green function. This algorithm is applied to investigate the effects of electrons onsite Coulomb repulsion on the band structure of a square lattice in both single-site approximations such as dynamical mean field theory (DMFT) and multi-site approximations such as effective medium supercell approximation (EMSCA). The advantages of our algorithm in comparison to the Hirsch-Fye algorithm and also the Blankenbecler, Scalapino, and Sugar (BSS) algorithm are the elimination of instabilities resulting from the Metropolis algorithm in the accepting and rejecting configurations, stability at low temperatures, the elimination of systematic errors resulting from the update of the Green's function in the quantum Monte Carlo process, and considering different probabilities for each possible configuration. Finally, by using our algorithm, it is possible to calculate the interacting three-dimensional system's band structure and the density of states that obey the Hubbard model. We have applied our algorithm to an interactive two-dimensional square lattice. As a result, phase transition boundaries can be easily recognized through calculated bands for different repulsions. Our results show that critical Coulomb repulsion values for Mott transition are uc=9.05t and uc=2.4t for DMFT and BEMSCA respectively. This means that DMFT significantly overestimates band splitting due to electrons' Coulomb repulsion. We found by starting at low repulsions and then increasing electrons' Coulomb repulsion, a partially flatted valance band around the center of the first Brillouin zone appears, but disappears at high repulsions.
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 $\ensuremath{\Delta}\ensuremath{\equiv}0.$