Quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Abstract

Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (∆). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/∆ is increased. Since it is known that at ∆ = 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 ∆ and (ii) decreasing ∆ at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential ∆. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition.

Quantum critical behavior of the one-dimensional ionic Hubbard model

“…Variational and Green's function Quantum Monte Carlo (QMC) data obtained for the BO parameter, the electric polarization, and the localization length were interpreted in favor of a scenario with a single critical point U c and finite BO for U > U c . 9 In a different calculation using auxiliary field QMC, data for the one-particle spectral weight were argued to show two critical points with an intermediate metallic phase. 10 Exact diagonalization studies of the Berry phase 11 and energy gaps 12,13,14 have been interpreted as favoring one critical point 13 or two points; 11 in two investigations this issue was left unresolved.…”

Variational Approach to Localization Length for Two-Dimensional Hubbard Model

“…λ N represents how electrons can broaden in an insulating state; we can judge that the system is insulating (metallic), if λ N remains finite (diverges) as the system size is increased to infinity. Thus, a Mott transition point can be determined by the diverging point of λ N , without carrying out differentiating operations in contrast to D. In early studies for one-dimensional systems, λ N or a corresponding susceptibility was calculated using exact diagonalization [11], quantum Monte Carlo method [12], and density matrix renormalization group [13]. Regarding VMC, λ N was calculated for a hydrogen chain [14]; it seems that λ N can be a good measure.…”

Localization lengths over metal to band insulator transitions

“…(29) is well suited to evaluating the localization length within the framework of quantum Monte Carlo [22] and has been applied previously [9,13]. As with the evaluation of any quantity with Monte Carlo methods, there is an associated statistical error and some examination of its behaviour is required, especially in cases where the localization length is large.…”

“…Among the exceptions are two quantum Monte Carlo (QMC) studies, one of phase transitions in the one-dimensional ionic Hubbard model [13], and one of the dielectric response of periodic systems [9]. In the latter, it was observed that the inclusion of many-body correlation effects dramatically affected the value of the polarizability and improved its convergence with system size by decreasing the localization length, a conclusion supported by calculations in which self-interaction corrections were included in calculations of Born effective charges [14].…”