Simulating a chiral gauge theory

Abstract

Chiral gauge theories underlie the Standard Model, yet none has been simulated nonperturbatively. Lattice constructions that evade the Nielsen-Ninomiya obstruction entail complex fermion measures or infinite-dimensional local Hilbert spaces. Here we provide a gauge-invariant Hamiltonian lattice regularization of 1+1-dimensional abelian chiral gauge theories built from clock-and-shift qudits with $\mathbb{Z}_N$ gauge fields, in which the global chiral symmetry and its 't Hooft anomaly survive exactly mod $N$. Anomaly cancellation on the lattice lets the Gauss laws be imposed and solved exactly, reducing the theory to an unconstrained qudit chain. Using infinite matrix product states, we simulate the canonical 1+1-dimensional chiral gauge theory, the 34-50 model, and find excellent agreement with analytic predictions, showing that a finite-dimensional local Hilbert space at $N=6$ reproduces the expected infrared physics of the continuum 34-50 model. This provides an efficient and practical solution to the problem of simulating general abelian chiral gauge theories in 1+1 dimensions, both on classical and quantum computers.