Excitation spectra and spin gap of the half-filled Holstein-Hubbard model

TL;DR

This paper investigates the excitation spectra and spin gap of the half-filled Holstein-Hubbard model using quantum Monte Carlo, revealing different phases with distinct spectral and excitation properties, including evidence for a persistent spin gap.

Contribution

It provides the first detailed numerical analysis of excitation spectra and spin gaps in the Holstein-Hubbard model across various phases, clarifying the nature of metallic and insulating states.

Findings

Metallic phase consistent with Luther-Emery liquid with gapped spin and single-particle excitations

Mott phase exhibits charge gap and gapless spin excitations

Peierls state shows gaps in charge, spin, and single-particle spectra, plus soliton excitations

Abstract

Single-- and two-particle excitation spectra of the one-dimensional, half-filled Holstein-Hubbard model are calculated using the continuous-time quantum Monte Carlo method. In the metallic phase, the results are consistent with a Luther-Emery liquid that has gapped spin and single-particle excitations but a gapless charge mode. However, given the initially exponential dependence of the spin gap on the backscattering matrix element, the numerical excitation spectra appear gapless in the weak-coupling regime, and therefore resemble those of a Luttinger liquid. The Mott phase has the expected charge gap and gapless spin excitations. The Peierls state shows a charge, spin and single-particle gap, a soft phonon mode, backfolded shadow bands and soliton excitations. Arguments and numerical evidence for the existence of a nonzero spin gap throughout the metallic phase are provided in terms of equal-time spin and charge correlation functions.