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Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

by Katja Klobas, Bruno Bertini

Submission summary

As Contributors: Bruno Bertini · Katja Klobas
Preprint link: scipost_202104_00016v1
Date submitted: 2021-04-14 10:25
Submitted by: Klobas, Katja
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


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.

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Submission scipost_202104_00016v1 on 14 April 2021

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