Thermalization of Gauge Theories from their Entanglement Spectrum

TL;DR

This paper investigates the entanglement structure and thermalization process in (2+1)-dimensional Z2 lattice gauge theories, confirming theoretical conjectures and characterizing the dynamics leading to thermal equilibrium.

Contribution

It demonstrates the entanglement spectrum's properties, confirms Li and Haldane's conjecture, and provides a detailed description of thermalization stages in Z2 gauge theory.

Findings

Confirmed Li and Haldane's conjecture for the entanglement spectrum.

Showed the entanglement Hamiltonian's consistency with the Bisognano-Wichmann theorem.

Described the characteristic stages of thermalization, including entropy saturation.

Abstract

Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the Entanglement Structure of $\mathbf{Z}_2$ lattice gauge theory in $(2+1)$ spacetime dimensions. We demonstrate Li and Haldane's conjecture, and show consistency of the Entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying non-equilibrium dynamics after a quench, we provide an extensive description of thermalization in $\mathbf{Z}_2$ gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients $\alpha = 0.8 \pm 0.2$ and $ \beta = 0.0 \pm 0.1$ at intermediate times, and finally thermal saturation of the von Neumann entropy.