Domain Wall Fermions for Planar Physics

TL;DR

This paper develops lattice formulations for 2+1D Dirac fermions that preserve key symmetries, introduces a domain wall approach, and provides numerical evidence of symmetry restoration in the continuum limit.

Contribution

It generalizes the Ginsparg-Wilson relation to 2+1D fermions, formulates a domain wall approach, and demonstrates symmetry recovery through numerical simulations.

Findings

U(2N) symmetry is recovered as domain-wall separation increases.

Formulations preserve global symmetries up to lattice spacing corrections.

Numerical evidence supports the continuum limit behavior.

Abstract

In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations which preserve the global U(2N ) symmetry present in the massless limit, and its breakdown to U(N)xU(N) implemented by three independent and parity-invariant fermion mass terms. I set out generalisations of the Ginsparg-Wilson relation, leading to a formulation of an overlap operator, and explore the remnants of the global symmetries which depart from the continuum form by terms of order of the lattice spacing. I also define a domain wall formulation in 2+1+1d, and present numerical evidence, in the form of bilinear condensate and meson correlator calculations in quenched non-compact QED using reformulations of all three mass terms, to show that U(2N) symmetry is recovered in the limit that the domain-wall separation tends to infinity. The possibility that overlap and domain wall formulations of reducible fermions may coincide only in the continuum limit is discussed.