Thermalization and localization in discretized quantum field theory

The von Neumann entanglement entropy of a sub-region in an out-of-equilibrium many-body quantum system evolves in time. For the late-time steady state, a “volume” law behavior typically indicates thermalization, whereas memory of the initial state (such as an “area” law behavior) may indicate localization. In this talk, I will discuss these two phases in the context of discretized scalar quantum field theory in two and four spacetime dimensions in the absence/presence of disorder. I will restrict to Gaussian initial states with linear dynamics and obtain exact results using the covariance matrix (whose dimension scales linearly with system size). I will first review the results for a mass quench in the free theory where the entanglement entropy grows linearly in time, saturating to a volume law behavior. I will next introduce a local disorder term in the Hamiltonian and show that, for sufficiently large disorder strength, the growth of entanglement entropy is suppressed, preserving the initial state behavior. I will finally discuss the continuum limit and how it affects measures such as the gap ratio.