Thermalization dynamics in many-body Floquet dynamics via the influence matrix approach

The influence matrix approach to quantum many-body dynamics aims at describing the effect of a system on the non-equilibrium evolution of a local subsystem. Using a combination of analytical insights and matrix-product states computations, we characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description for interfering intervals of local quantum trajectories. We illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The approach formulated here provides an intuitive view of the quantum many-body dynamics problem, allows to construct models of thermalizing dynamics that are solvable or can be efficiently treated by tensor-network methods, and to further characterize quantum ergodicity or lack thereof.