Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics

TL;DR

This study uses Langevin dynamics and quantum Monte Carlo to explore phase transitions in the 2D SSH model, revealing a transition from valence bond solid to antiferromagnetic order driven by phonon frequency.

Contribution

It introduces an efficient Langevin dynamics approach for the 2D SSH model and demonstrates a phonon-driven transition between valence bond solid and antiferromagnetic phases.

Findings

Transition from valence bond solid to antiferromagnetism with increasing phonon frequency

Renormalization of electronic band structure indicating a gapped polaronic band

Presence of gapless modes linked to long-range order

Abstract

The two-dimensional Su-Schrieffer-Heeger model of electrons coupled to quantum phonons is investigated using Langevin dynamics within the framework of auxiliary-field quantum Monte Carlo. Based on an explicit determination of the density of zeros of the fermion determinant, it is argued that the method is efficient in the challenging adiabatic limit. Large-scale simulations at the O(4)-symmetric point establish that the ground state of the 2D SSH model undergoes a transition from a $(\pi,\pi)$ valence bond solid to an antiferromagnet with increasing phonon frequency, yet still in the adiabatic regime. The single-particle spectrum illustrates the renormalization of the electronic band and suggests the existence of a gapped polaronic band, whereas the particle-hole channels show gapless modes associated with long-range bond and magnetic order, respectively. The simulations are supplemented with a mean-field analysis and a self-consistent Born proximation.