# Effect of Strain on Charge Density Wave Order in the Holstein Model

## TL;DR

This study uses Quantum Monte Carlo simulations and mean-field theory to analyze how anisotropic strain affects charge density wave order in the Holstein model, revealing that transition temperature remains stable at low strain but decreases at higher strain.

## Contribution

It provides new insights into the strain dependence of charge density wave order in the Holstein model through combined computational and theoretical approaches.

## Key findings

- CDW transition temperature is stable at moderate strain
- Density correlations change significantly with strain
- Charge ordering transition is detectable via density of states at large strain

## Abstract

We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-\delta, 1 + \delta$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $\delta \lesssim 0.3$, but begins to decrease more rapidly at $\delta \gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $\delta$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $\delta$ and a more rapid decrease for larger strains. We also obtain the density of states $N(\omega)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter.