Chern insulator transitions with Wilson fermions on a hyperrectangular lattice

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.

arXiv comment28 pages, 9 figures, references updated

References in corpus (28)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• A Method for Simulating Chiral Fermions on the Lattice
• The glueball spectrum from an anisotropic lattice study
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Chiral Fermions from Lattice Boundaries
• Classification and analysis of two dimensional abelian fractional topological insulators
• Chern-Simons Currents and Chiral Fermions on the Lattice
• The Anisotropic Wilson Gauge Action
• Charmonium Spectrum from Quenched Anisotropic Lattice QCD
• Charmed baryons in lattice QCD
• Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum
• Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Improving Lattice Quark Actions
• Chiral Fermions and Anomalies on a Finite Lattice
• Critical Momenta of Lattice Chiral Fermions
• Dynamical simulation of N=1 supersymmetric Yang-Mills theory with domain wall fermions
• Lattice study on kaon nucleon scattering length in the I=1 channel
• Hadron Scattering in an Asymmetric Box
• New Domain-Wall Fermion Actions
• I=2 Pion scattering length with improved actions on anisotropic lattices
• Gauge Theories on a 2+2 Anisotropic Lattice
• Fractional quantum Hall effect in a relativistic field theory
• Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices
• Effective Field Theory for the Anisotropic Wilson Lattice Action

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• Chiral fermions on lattice axion strings
• Correlated Chern insulators in two-dimensional Raman lattices: a cold-atom regularization of strongly-coupled four-Fermi field theories