A Fully Gauge-Fixed SU(2) Hamiltonian for Quantum Simulations

TL;DR

This paper presents a fully gauge-fixed SU(2) lattice gauge theory Hamiltonian that simplifies quantum simulations by isolating total charge sectors and enabling efficient, polynomial-scaling quantum resource requirements.

Contribution

It introduces a novel gauge-fixing method using a geometric picture and Euler angles, enabling efficient simulation across all coupling regimes.

Findings

Hilbert space partitions into sectors with different total angular momentum.

Gauge-fixing to the total charge-zero sector is straightforward.

Quantum resources scale polynomially with lattice volume.

Abstract

We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new `sequestered' basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.