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  • Letter
  • Open Access

Transport and entanglement growth in long-range random Clifford circuits

Jonas Richter1,2,3, Oliver Lunt4,5, and Arijeet Pal1

  • 1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • 2Department of Physics, Stanford University, Stanford, California 94305, USA
  • 3Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
  • 4Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
  • 5School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

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Phys. Rev. Research 5, L012031 – Published 3 March, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012031

Abstract

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U(1) symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to S(t)∝t1/z where the dynamical transport exponent z depends on the probability ∝r−α of gates spanning a distance r. For sufficiently small α, we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator spreading in U(1)-symmetric Clifford circuits where the emerging light cones can be understood in the context of classical Lévy flights. Our Letter sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics.

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Phys. Rev. Research 5, L012031– Published 3 March, 2023
  • Received 30 May 2022
  • Accepted 3 February 2023
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