Applications of lattice QCD techniques for condensed matter systems

TL;DR

This paper reviews how lattice QCD techniques, especially Hybrid Monte-Carlo simulations, are applied to study strongly interacting condensed matter systems like graphene, topological insulators, and semi-metals, providing insights into their quantum behaviors.

Contribution

It introduces the application of lattice QCD methods to condensed matter physics and discusses recent simulation results and open problems in the field.

Findings

HMC simulations elucidate the semi-metal behavior of graphene.

Application of lattice techniques to topological insulators and semi-metals.

Identification of open physical problems in condensed matter systems.

Abstract

We review the application of lattice QCD techniques, most notably the Hybrid Monte-Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a basic introduction into the HMC algorithm as applied to condensed matter systems, we review HMC simulations of graphene, which in the recent years have helped to understand the semi-metal behavior of clean suspended graphene at the quantitative level. We also briefly summarize other novel physical results obtained in these simulations. Then we comment on the applicability of Hybrid Monte-Carlo to topological insulators and Dirac and Weyl semi-metals and highlight some of the relevant open physical problems. Finally, we also touch upon the lattice strong-coupling expansion technique as applied to condensed matter systems.