Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function

TL;DR

This study uses a variational Monte Carlo approach with a backflow-inspired wave function to explore insulating and metallic phases in a one-dimensional Hubbard-Su-Schrieffer-Heeger model, revealing novel gap behaviors and phase transitions.

Contribution

It introduces a generalized Jastrow-Slater wave function incorporating electron-phonon coupling, providing new insights into phase behavior in 1D electron-phonon systems with repulsive interactions.

Findings

Half-filling: Mott insulator or Peierls insulator phases.

Doping: charge gap closes, leading to Luttinger liquid or spin-gapped metal.

Evidence of a phase with gapless charge and gapped spin excitations.

Abstract

The interplay between electron-electron and electron-phonon interactions is studied in a one-dimensional lattice model, by means of a variational Monte Carlo method based on generalized Jastrow-Slater wave functions. Here, the fermionic part is constructed by a pair-product state, which explicitly depends on the phonon configuration, thus including the electron-phonon coupling in a backflow-inspired way. We report the results for the Hubbard model in presence of the Su-Schrieffer-Heeger coupling to optical phonons, both at half-filling and upon hole doping. At half-filling, the ground state is either a translationally invariant Mott insulator, with gapless spin excitations, or a Peierls insulator, which breaks translations and has fully gapped excitations. Away from half-filling, the charge gap closes in both Mott and Peierls insulators, turning the former into a conventional Luttinger liquid (gapless in all excitation channels). The latter, instead, retains a finite spin gap that closes only above a threshold value of the doping. Even though consistent with the general theory of interacting electrons in one dimension, the existence of such a phase (with gapless charge but gapped spin excitations) has never been demonstrated in a model with repulsive interaction and with only two Fermi points. Since the spin-gapped metal represents the one-dimensional counterpart of a superconductor, our results furnish evidence that a true off-diagonal long-range order may exist in the two-dimensional case.