Charge Order in the Holstein Model on a Honeycomb Lattice

TL;DR

This study uses determinant quantum Monte Carlo to investigate how electron-phonon interactions induce charge density wave order in the Holstein model on a honeycomb lattice, revealing a finite critical interaction strength for the transition.

Contribution

It provides the first detailed quantum Monte Carlo analysis of charge order in the Holstein model on a honeycomb lattice, highlighting the role of electron-phonon interactions.

Findings

Charge density wave order appears only above a finite critical interaction strength.

The transition temperature for CDW can be finite due to discrete symmetry breaking.

Electron-phonon interactions significantly influence Dirac fermions on the honeycomb lattice.

Abstract

The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on a Honeycomb lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.