Gauge equivariant neural networks for quantum lattice gauge theories

TL;DR

This paper introduces gauge equivariant neural networks that exactly incorporate local gauge symmetries to efficiently simulate quantum lattice gauge theories, capturing phase transitions and ground states.

Contribution

It develops gauge equivariant neural-network quantum states that satisfy local gauge constraints and applies them to Z2 gauge theories on lattices, demonstrating their effectiveness.

Findings

Successfully model ground states of Z2 lattice gauge theories

Capture confining and deconfining phase transitions

Provide compact variational representations of quantum states

Abstract

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wavefunction for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining/deconfining phase transition of the Wilson loop order parameter.