Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study

TL;DR

This study uses hybrid Monte Carlo simulations to investigate charge density wave order in the Holstein model on a kagome lattice, revealing a specific ordered phase at 2/3 filling and estimating its transition temperature.

Contribution

It provides the first evidence of $ ext{sqrt{3}} imes ext{sqrt{3}}$ CDW order in the kagome Holstein model using a novel hybrid Monte Carlo method.

Findings

CDW order at 2/3 filling with wavevector at K-points

Transition temperature estimated at T_c ≈ t/18

No CDW order detected at other fillings or temperatures T ≥ t/20

Abstract

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for $\sqrt{3} \times \sqrt{3}$ CDW order at an average electron filling of $\langle n \rangle =2/3$ per site, with an ordering wavevector at the $K$-points of the Brillouin zone. We estimate a phase transition occurring at $T_{c}\approx t/18$, where $t$ is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures $T \geq t/20$.