Thermalization of Gauge Theories from their Entanglement Spectrum

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 $\hat{I}\pm =0.8\pm 0.2$ and ${\hat{I}}^2=0.0\pm 0.1$ at intermediate times, and finally thermal saturation of the von Neumann entropy.

Journal version: additional numerical finite volume studies included; improved error estimates; references updated; 11 pages, 8 figures