Quantum phase transitions on the hexagonal lattice

TL;DR

This paper reviews the current progress in using Hybrid Monte Carlo simulations to study quantum phase transitions in Hubbard models on the hexagonal lattice, relevant for materials like graphene.

Contribution

It provides an overview of recent advancements in applying first-principles Hybrid Monte Carlo methods to explore phase structures of Hubbard models on the hexagonal lattice.

Findings

Progress in simulating phase transitions

Insights into electronic properties of graphene

Development of simulation techniques

Abstract

Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction.