Gauge Theory Couplings on Anisotropic Lattices

TL;DR

This paper derives perturbative relations for gauge theory couplings on anisotropic lattices, reducing classical preprocessing for quantum simulations and validating results with nonperturbative and Monte Carlo methods.

Contribution

It provides a general perturbative framework for relating bare and renormalized quantities at any anisotropy, applicable to various gauge groups, aiding quantum lattice simulations.

Findings

Less than 10% discrepancy with nonperturbative results for SU(2) and U(1).

Perturbative results agree with Monte Carlo simulations for discrete groups.

Framework reduces classical preprocessing needed for quantum simulations.

Abstract

The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near the Hamiltonian limit can be used for setting the lattice spacings in real-time through analytical continuation, thereby reducing errors in quantum simulations. In this work, we derive perturbative relations between bare and renormalized quantities in Euclidean spacetime at any anisotropy factor -- the ratio of spatial to temporal lattice spacings -- and in any spatial dimension for $U(N)$ and $SU(N)$. This reduces the required classical preprocessing for quantum simulations. We find less than $10\%$ discrepancy between our perturbative results and those from existing nonperturbative determinations of the anisotropy for $SU(2)$ and $U(1)$ gauge theories. For the discrete groups $\mathbb{Z}_{10}$, $\mathbb{Z}_{100}$ and $\mathbb{BI}$, we perform lattice Monte Carlo simulations to extract anisotropy factors and observe similar agreement with our perturbative results.