SciPost Phys. 11, 107 (2021) ·
published 20 December 2021
We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.
SciPost Phys. 11, 106 (2021) ·
published 20 December 2021
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.
SciPost Phys. Core 2, 010 (2020) ·
published 26 June 2020
In this paper we study the space evolution in the Rule 54 reversible cellular
automaton, which is a paradigmatic example of a deterministic interacting
lattice gas. We show that the spatial translation of time configurations of the
automaton is given in terms of local deterministic maps with the support that
is small but bigger than that of the time evolution. The model is thus an
example of space-time dual reversible cellular automaton, i.e. its dual is also
(in general different) reversible cellular automaton. We provide two equivalent
interpretations of the result; the first one relies on the dynamics of
quasi-particles and follows from an exhaustive check of all the relevant time
configurations, while the second one relies on purely algebraic considerations
based on the circuit representation of the dynamics. Additionally, we use the
properties of the local space evolution maps to provide an alternative
derivation of the matrix product representation of multi-time correlation
functions of local observables positioned at the same spatial coordinate.