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 nonequilibrium 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.

• Eigenstate thermalization
• Entanglement in field theory
• Gauge theories
• Lattice gauge theory
• Topological phases of matter
• 2-dimensional systems
• Nonequilibrium systems