Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models

TL;DR

This paper investigates the excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models using quantum Monte Carlo, revealing phase transitions, spectral gaps, and degeneracies in both spinless and spinful cases, and comparing acoustic and optical phonon effects.

Contribution

It provides a comprehensive analysis of quantum SSH models with phonons, demonstrating the equivalence of acoustic and optical phonon effects and detailing phase transitions and spectral properties.

Findings

Identical results for SSH models with acoustic and optical phonons within errors.

Observation of Peierls transition related to Kosterlitz-Thouless transition.

Identification of spin and charge gaps and degeneracies in spinful SSH models.

Abstract

We study one-dimensional Su-Schrieffer-Heeger (SSH) models with quantum phonons using a continuous-time quantum Monte Carlo method. Within statistical errors, we obtain identical results for the SSH model with acoustic phonons, and a related model with a coupling to an optical bond phonon mode. Based on this agreement, we first study the Peierls metal-insulator transition of the spinless SSH model, and relate it to the Kosterlitz-Thouless transition of a spinless Luttinger liquid. In the Peierls phase, the spectral functions reveal the single-particle and charge gap, and a central peak related to long-range order. For the spinful SSH model, which has a dimerized ground state for any nonzero coupling, we reveal a symmetry-related degeneracy of spin and charge excitations, and the expected spin and charge gaps as well as a central peak. Finally, we study the SSH-$UV$ model with electron-phonon and electron-electron interaction. We observe a Mott phase with critical spin and bond correlations at weak electron-phonon coupling, and a Peierls phase with gapped spin excitations at strong coupling. We relate our findings to the extended Hubbard model, and discuss the physical origin of the agreement between optical and acoustic phonons.