Hamiltonian limit of lattice QED in 2+1 dimensions

TL;DR

This paper investigates the Hamiltonian limit of lattice QED in 2+1 dimensions by extrapolating anisotropic lattice results, aiming to connect classical and quantum computational approaches.

Contribution

It introduces methods to determine the Hamiltonian limit using anisotropic lattice simulations and explores the gradient flow approach for future quantum-classical hybrid studies.

Findings

Computed the renormalized anisotropy $\xi_R$ using multiple methods

Established a procedure to reach the Hamiltonian limit in lattice QED3

Provided insights for combining quantum and classical lattice computations

Abstract

The Hamiltonian limit of lattice gauge theories can be found by extrapolating the results of anisotropic lattice computations, i.e., computations using lattice actions with different temporal and spatial lattice spacings ($a_t\neq a_s$), to the limit of $a_t\to 0$. In this work, we present a study of this Hamiltonian limit for a Euclidean $U(1)$ gauge theory in 2+1 dimensions (QED3), regularized on a toroidal lattice. The limit is found using the renormalized anisotropy $\xi_R=a_t/a_s$, by sending $\xi_R \to 0$ while keeping the spatial lattice spacing constant. We compute $\xi_R$ in $3$ different ways: using both the ``normal'' and the ``sideways'' static quark potential, as well as the gradient flow evolution of gauge fields. The latter approach will be particularly relevant for future investigations of combining quantum computations with classical Monte Carlo computations, which requires the matching of lattice results obtained in the Hamiltonian and Lagrangian formalisms.