Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

TL;DR

This study uses quantum Monte Carlo simulations to explore how increasing phonon frequency in the one-dimensional quarter-filled Holstein model causes a ground state transition from charge order to superfluid pairing, indicating bipolaron formation.

Contribution

It provides the first detailed numerical analysis of the Peierls to superfluid crossover in the 1D Holstein model, highlighting the role of phonon frequency in pairing mechanisms.

Findings

Ground state shifts from charge order to pairing with increasing phonon frequency.

Existence of a spin gap across the crossover.

Evidence of bipolaron formation and condensation.

Abstract

We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order---2k_F charge correlations---to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phonon frequencies. The crossover can hence be interpreted in terms of preformed pairs corresponding to bipolarons, which are essentially localised in the Peierls phase, and "condense" with increasing phonon frequency to generate dominant pairing correlations.