Lattice Field Theory Study of Magnetic Catalysis in Graphene

TL;DR

This paper uses lattice gauge theory simulations to study magnetic catalysis in graphene, focusing on chiral symmetry breaking, mass spectrum, and the challenges of analyzing time-reversal-odd condensates.

Contribution

It presents a nonperturbative lattice simulation approach to investigate magnetic catalysis and chiral symmetry breaking in graphene's effective field theory.

Findings

Observation of chiral condensate formation under magnetic field

Identification of Nambu-Goldstone mode in the mass spectrum

Discussion of difficulties in studying time-reversal-odd condensates

Abstract

We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. Our fully nonperturbative calculation uses methods of lattice gauge theory to study the theory using a hybrid Monte Carlo approach. We investigate the phenomenon of magnetic catalysis in the context of graphene by studying the chiral condensate which is the order parameter characterizing the spontaneous breaking of chiral symmetry. In the EFT, the symmetry breaking pattern is given by $U(4) \to U(2) \times U(2)$. We also comment on the difficulty, in this lattice formalism, of studying the time-reversal-odd condensate characterizing the ground state in the presence of a magnetic field. Finally, we study the mass spectrum of the theory, in particular the Nambu-Goldstone (NG) mode as well as the Dirac quasiparticle, which is predicted to obtain a dynamical mass.