Dynamical chirality production in one dimension

TL;DR

This paper explores how to compute dynamical chirality production in a one-dimensional lattice gauge theory, providing a simplified formulation that captures the chiral anomaly, demonstrated through classical emulation.

Contribution

It introduces a simplified formalism for calculating chirality production on a 1D lattice, enabling clearer extraction of the chiral anomaly in lattice gauge theories.

Findings

Successfully computed chirality production in a 1D lattice gauge theory

Demonstrated the formalism on a $Z_2$ gauge theory using classical emulation

Provided insights into the relation between lattice chirality and continuous chiral anomaly

Abstract

We discuss the quantum computation of dynamical chirality production in lattice gauge theory. Although the chirality of a lattice fermion is complicated in general dimensions, it can be simply formulated on a one-dimensional lattice. The chiral fermion formalism enables us to extract the physical part of the chirality production that would be interpreted as the chiral anomaly in the continuous theory. We demonstrate the computation of the $Z_2$ lattice gauge theory on a classical emulator.