Toward a Ginsparg-Wilson Lattice Hamiltonian

TL;DR

This paper develops an approximate Ginsparg-Wilson Hamiltonian for lattice QCD that preserves chiral symmetry, is free of doublers, and works in odd spatial dimensions, with explicit results in one dimension.

Contribution

It introduces a novel approximate Hamiltonian satisfying the Ginsparg-Wilson equation suitable for quantum chromodynamics simulations.

Findings

Hamiltonian is non-local and contains ghosts.

It is free of fermion doublers.

Correct continuum limit achieved.

Abstract

To address quantum computation of quantities in quantum chromodynamics (QCD) for which chiral symmetry is important, it would be useful to have the Hamiltonian for a fermion satisfying the Ginsparg-Wilson (GW) equation. I work with an approximate solution to the GW equation which is fractional linear in time derivatives. The resulting Hamiltonian is non-local and has ghosts, but is free of doublers and has the correct continuum limit. This construction works in general odd spatial dimensions, and I provide an explicit expression for the Hamiltonian in 1 spatial dimension.