Entanglement Properties of SU(2) Gauge Theory

TL;DR

This paper reviews recent numerical studies on the thermalization process in (2+1)-dimensional SU(2) gauge theory, highlighting entanglement dynamics, spectral properties, and implications for quantum advantage.

Contribution

It provides new insights into entanglement entropy, spectral form factors, and the absence of quantum scars in SU(2) gauge theory, advancing understanding of thermalization in nonabelian gauge fields.

Findings

Entanglement entropy transitions from area to volume scaling with energy.

Spectral form factor shows expected late-time behavior.

Maximum 'magic' measure occurs during thermalization.

Abstract

We review recent and present new results on thermalization of nonabelian gauge theory obtained by exact numerical simulation of the real-time dynamics of $(2+1)$-dimensional SU(2) lattice gauge theory. We discuss: (1) tests confirming the Eigenstate Thermalization Hypothesis; (2) the entanglement entropy of sublattices, including the Page curve, the transition from area to volume scaling with increasing energy of the eigenstate and its time evolution that shows thermalization of localized regions to be a two-step process; (3) the absence of quantum many-body scars when higher gauge field representations are taken into account; (4) the spectral form factor, which exhibits the expected slope-ramp-plateau structure for late times; (5) the entanglement Hamiltonian for SU(2), which has properties in accordance with the Bisognano-Wichmann theorem; and (6) a measure for non-stabilizerness or ``magic'' that is found to reach its maximum during thermalization. We conclude that the thermalization of nonabelian gauge theories is a promising process to establish quantum advantage.