Chern insulator transitions with Wilson fermions on a hyperrectangular lattice

TL;DR

This paper explores how lattice anisotropy in a 2+1D Wilson fermion model induces topological phase transitions and chiral edge modes without the need for domain walls, extending understanding of topological phases in lattice gauge theories.

Contribution

It demonstrates that lattice anisotropy alone can cause topological phase transitions and chiral edge modes in Wilson fermion models, without domain walls in mass.

Findings

Anisotropic lattice spacing leads to distinct topological phases.

Chiral edge modes can occur without mass domain walls.

Zero mode properties change with lattice anisotropy.

Abstract

A $U(1)$ gauge theory coupled to a Wilson fermion on a $2+1$ dimensional cubic lattice is known to exhibit Chern insulator like topological transitions as a function of the the ratio $M/R$ where $M$ is the fermion mass and $R$ is the Wilson parameter. I show that, with $M$ and $R$ held fixed, a rectangular lattice with anisotropic lattice spacing can exhibit distinct topological phases as a function of the lattice anisotropy. As a consequence, a $2+1$ dimensional lattice theory without any domain wall in the fermion mass can still exhibit chiral edge modes on a $1+1$ dimensional defect across which lattice spacing changes abruptly. Likewise, a domain wall in the fermion mass on a uniform rectangular lattice can exhibit discrete changes in the number and chirality of zero modes as a function of lattice anisotropy. The construction presented in this paper can be generalized to higher dimensional space-time lattices.