One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling

Abstract

The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at halffilling, increasing the coupling g to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction U drives the fermions into a Mott antiferromagnet. At low g and U , or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range ξ, interpolating between the Holstein and Fröhlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range ξ, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction U will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the U = 0 case, even for small values of the coupling range.

Competition between phase separation and spin density wave or charge density wave order: Role of long-range interactions

“…1 are consistent with those obtained at V = 0 in Ref. [53], which uses the alternate stochastic Green function [60] method.…”

“…The solution to this dilemma in the general case is clear-the inclusion of non-zero electronelectron repulsion. A recent study which incorporates on-site U but retains V = 0 [53] revealed continued phase separation over much of the phase diagram, with SDW occurring only if ξ and λ 0 were rather small. We show here that V can significantly stabilize the CDW and SDW phases against collapse of the density.…”

Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons

“…For λ = 0.1, the slope is -0.9876 with R 2 = 0.9993 and for λ = 1.0, the slope is -0.8617 with R 2 = 0.9942. conditioned action leads to a long autocorrelation time that scales quadratically with increasing ω −1 . There have been attempts to ameliorate this problem based on global moves such as the Langevin dynamics approach 57,89,94 and the self-learning Monte Carlo approach. 95 We also mention that the work of Hohenadler and co-workers removed the autocorrelation problem using the Lang-Firsov transformation along with a principal component analysis.…”

One-dimensional Peierls phase separation in the dilute carrier density limit

“…However, no effective phonon-mediated longer-range attraction between Holstein bipolarons exists and so phase separation does not occur. We note that phase separation occurring at or near half-filling in local electron-phonon models [39][40][41][42] -while interesting -has no relevance to the current work, which focuses on extremely dilute systems. For a non-exhaustive list of literature relevant to polaronic phenomena in the Peierls model, see [43][44][45][46].…”