Gauge Equivariant Neural Networks for Quantum Lattice Gauge Theories
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 manybody quantum systems with exact local gauge invariance, gauge equivariant neuralnetwork quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Z_{d} gauge group and nonAbelian Kitaev D (G ) models on different geometries. Focusing on the special case of Z_{2} gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loopgas solution as a special case. Gauge equivariant neuralnetwork quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wave function for the Z_{2} theory away from the exactly solvable limit, and to demonstrate the confining or deconfining phase transition of the Wilson loop order parameter.
 Publication:

Physical Review Letters
 Pub Date:
 December 2021
 DOI:
 10.1103/PhysRevLett.127.276402
 arXiv:
 arXiv:2012.05232
 Bibcode:
 2021PhRvL.127A6402L
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Machine Learning;
 High Energy Physics  Lattice;
 Quantum Physics
 EPrint:
 doi:10.1103/PhysRevLett.127.276402