Exact Hidden Markovian Dynamics in Quantum Circuits

Characterizing non-equilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this talk, I will introduce a novel class of systematically constructed solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem dynamics. This feature enables accurately calculating the thermalization dynamics of local observables and the growth of entropy for arbitrary evolution time. Utilizing the influence matrix method, I will show that the influence of the time-evolved global system on a finite subsystem can be analytically described by sequential, time-local quantum channels acting on the subsystem with an ancilla of finite Hilbert space dimension. I will present several concrete examples with varying local Hilbert space dimensions to demonstrate this approach.