Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry

TL;DR

This paper develops a family of Ginsparg-Wilson Hamiltonians with enhanced chiral symmetry properties, using higher-order relations to improve chiral charge conservation while maintaining anomaly reproduction, beneficial for quantum simulations.

Contribution

It introduces a new class of Hamiltonian lattice regularizations based on higher-order Ginsparg-Wilson relations, providing tunable chiral symmetry features and insights into anomaly reproduction.

Findings

Constructed order-$k$ Hamiltonian overlap operators with improved chiral properties.

Demonstrated the conservation of a nonquantized chiral charge that approaches quantization as $k$ increases.

Highlighted potential advantages for quantum and tensor-network simulations.

Abstract

We construct a family of Ginsparg-Wilson Hamiltonians with improved chiral properties, starting from a construction of Creutz-Horvath-Neuberger that provides a doubler-free Hamiltonian lattice regularization for Dirac fermions in even spacetime dimensions. We use a higher-order generalization of the Ginsparg-Wilson relation due to Fujikawa, which yields an order-$k$ Hamiltonian overlap operator for each integer $k \geq 0$, with an exactly conserved but nonquantized chiral charge that becomes quantized as $k \to \infty$. Our construction provides physical insight into how Fujikawa's higher-order Ginsparg-Wilson relation improves chiral symmetry while reproducing the anomaly, highlighting the trade-offs inherent in any Hamiltonian lattice realization of an anomalous chiral symmetry. This class of Hamiltonian lattice regularizations, with their tunable chiral symmetry properties, offers potential advantages for quantum and tensor-network simulations.