Computing quantum thermalization dynamics: from quantum chaos to emergent hydro

Abstract

Computing the dynamics of strongly interacting quantum systems presents a fundamental challenge due to the growth of entanglement entropy in time. I will describe a new approach that overcomes this obstruction and captures chaotic dynamics and emergent hydrodynamic transport of quantum systems. Our scheme utilizes the time dependent variational principle with matrix product states to truncate “non-useful” entanglement. I will present new insights, obtained using the variational scheme, on quantum chaos on tensor networks, as well as new results pertaining to the many-body localization transition. If time permits I will offer an alternative perspective on the relation between quantum and classical chaos in many body systems, using a classical version of the Sachdev-Ye- Kitaev model. Chaos in this model is related to diverging geodesics on a SO(N) manifold equipped with a random metric. The quantum bound on chaos arises from a “chaotic mobility edge” in the classical Lyapunov spectrum, separating the lower part of the spectrum for which a classical chaos picture applies from the higher part of the spectrum for which quantum interference effects are strong enough to kill classical chaos.