Finite-size effects in Luther-Emery phases of Holstein and Hubbard models

TL;DR

This paper investigates finite-size effects in Luther-Emery phases of Holstein and Hubbard models, revealing how spin gaps influence numerical studies and proposing a bipolaron-based low-energy theory for the spinful Holstein model.

Contribution

It demonstrates the impact of spin gaps on finite-size numerical analyses and introduces a bipolaron-based low-energy theory for the spinful Holstein model.

Findings

Existence of a metallic phase with power-law charge correlations

Spin gap complicates finite-size numerical studies

Low-energy theory involves singlet bipolarons with mutual repulsion

Abstract

The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave (CDW) order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin gap significantly complicates finite-size numerical studies, and explains inconsistent previous results for Luttinger parameters and phase boundaries. On the other hand, no such complications arise in spinless models. The correct low-energy theory of the spinful Holstein model is argued to be that of singlet bipolarons with a repulsive, mutual interaction. This picture naturally explains the existence of a metallic phase, but also implies that gapless Luttinger liquid theory is not applicable.