Spin, charge and single-particle spectral functions of the one-dimensional quarter filled Holstein model

TL;DR

This study investigates the spin, charge, and spectral functions of the one-dimensional quarter-filled Holstein model using advanced quantum Monte Carlo methods, revealing a transition from Luttinger to Luther-Emery liquids and analyzing temperature-dependent spectral features.

Contribution

It introduces an extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to study spectral functions in the Holstein model, capturing phase transitions and temperature effects.

Findings

Transition from Luttinger to Luther-Emery liquid with increasing electron-phonon coupling

At high temperatures, spectral functions are well described by a self-consistent Born approximation

Low-temperature Luther-Emery phase exhibits a quasiparticle gap related to the spin gap

Abstract

We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon frequency $\omega_0 = 0.1 t$. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant $2k_f$ charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for within a self-consistent Born approximation. In the low temperature Luttinger liquid phase we observe features which compare favorably with a bosonization approach retaining only forward scattering. In the Luther-Emery phase, the spectral function at low temperatures shows a quasiparticle gap which matches half the spin gap whereas at temperatures above which this quasiparticle gap closes, characteristic features of the Luttinger liquid model are apparent. Our results are based on lattice simulations on chains up to L=20 for two-particle properties and on CDMFT calculations with clusters up to 12 sites for the single-particle spectral function.