Lattice chiral symmetry with hopping interactions

TL;DR

This paper introduces a Hamiltonian-based lattice formulation for Dirac fermions in 1+1 dimensions, using hopping interactions to resolve species doubling and approximate chiral symmetry, resulting in a close match to continuum behavior.

Contribution

It presents a novel lattice fermion formulation that employs hopping interactions to mitigate species doubling and realize approximate chiral symmetry.

Findings

Species doubling problem is effectively resolved.

Fermion propagator closely matches continuum results.

Approximate chiral symmetry is successfully implemented.

Abstract

We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator from the continuum one is small.