A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations

TL;DR

This paper presents a gauge redundancy-free formulation of compact QED with dynamical matter on lattices, simplifying the Hilbert space and constraints, which benefits numerical and quantum computational approaches.

Contribution

It introduces a dual representation of compact QED that eliminates gauge redundancies while preserving translational invariance, applicable in 2D and 3D lattices.

Findings

Dual representation in 2D is constraint-free.

In 3D, local constraints involve only gauge fields.

Reduced Hilbert space dimension for simulations.

Abstract

We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating frame, where the matter is decoupled from the gauge constraints, we can express the gauge field operators in terms of dual operators. In two space dimensions, the dual representation is completely free of any local constraints. In three space dimensions, local constraints among the dual operators remain but involve only the gauge field degrees of freedom (and not the matter degrees of freedom). These formulations, which reduce the required Hilbert space dimension, could be useful for both numerical (classical) Hamiltonian computations and quantum simulation or computation.