Abstract
We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.
Highlights
In this paper we adopt the time channel approach summarised in the previous section to describe the non-equilibrium dynamics of a specific integrable system: the reversible cellular automaton given by the Rule 54 in the classification of Ref. [87], which can be seen as a deterministic discrete-time limit of the Fredrickson-Andersen model [89]
In this paper we studied the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach
For the class of initial states considered, we showed that all local observables relax exponentially fast to Gibbs states
Summary
Over the last two decades intense efforts by both experimentalists and theorists have greatly advanced our understanding of isolated quantum matter out of equilibrium [1,2,3,4,5,6,7,8,9]. It is still unclear how and when the slow hydrodynamic regime is reached and what is the role played by the local conservation laws in the relaxation process This question is related to the more general problem of describing the dynamics of out-of-equilibrium quantum matter for large but finite times. A very interesting consequence of our results is that we can study exactly settings originating non-trivial transport of conservation laws at asymptotically large times, when the system is expected to follow the prediction of generalized hydrodynamics (GHD) [58, 59]. This gives the unprecedented possibility of testing this expectation. Several technical points and proofs are relegated to the two appendices
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