_ABSTRACT
When a generic isolated quantum many-body system is driven out of equilibrium, its local properties are eventually described by the thermal ensemble. This picture can be intuitively explained by saying that, in the thermodynamic limit, the system acts as a bath for its own local subsystems. Despite the undeniable success of this paradigm, for interacting systems most of the evidence in support of it comes from numerical computations in relatively small systems, and there are very few exact results. In the talk, I will present an exact solution for the thermalization dynamics in the "Rule 54" cellular automaton, which can be considered the simplest interacting integrable model. After introducing the model and its tensor-network formulation, I will present the main tool of my analysis: the space-like formulation of the dynamics. Namely, I will recast the time-evolution of finite subsystems in terms of a transfer matrix in space and construct its fixed-points. This construction provides the full description of subsystem dynamics and enables us to fully characterize relaxation time-scales. I will conclude by discussing the growth of entanglement after the quench, and show the agreement with the quasi-particle picture.
The talk is based on a recent series of papers: arXiv:2012.12256, arXiv:2104.04511, and arXiv:2104.04513.