On the semimetal-insulator transition and Lifshitz transition in simulations of mono-layer graphene

TL;DR

This paper reports on Hybrid-Monte-Carlo simulations of monolayer graphene, exploring the semimetal-insulator transition influenced by Coulomb interactions and the Lifshitz transition at finite density, highlighting finite-size effects and methodological approaches.

Contribution

It provides new simulation results on the critical coupling for the phase transition and preliminary insights into the Lifshitz transition at finite density in graphene.

Findings

Finite-size effects may influence the critical coupling estimate.

Evidence of a Lifshitz transition at finite Fermion-density.

Use of spin-dependent chemical potential to avoid sign problem.

Abstract

We report on the status of ongoing Hybrid-Monte-Carlo simulations of the tight-binding model of mono-layer graphene. We present results concerning the semimetal-insulator phase transition, whereby two-body interactions are modeled by a partially screened Coulomb potential which takes into account screening by electrons in the lower $\sigma$-orbitals. We obtain evidence that finite-size effects may still be present in the current estimate of the critical coupling strength $\alpha_C$, which was previously extracted from simulations on lattice-sizes up to $N_x=N_y=18$. We also present preliminary results concerning the Neck-disrupting Lifshitz transition which occurs at finite Fermion-density in the limit of vanishing two-body interactions. A sign-problem is circumvented by using a spin-dependent chemical potential in our simulations.