Transport and entanglement growth in long-range random Clifford circuits

• URL: http://arxiv.org/abs/2205.06309v2
• Date: Fri, 20 May 2022 14:09:03 GMT
• Title: Transport and entanglement growth in long-range random Clifford circuits
• Authors: Jonas Richter, Oliver Lunt, Arijeet Pal
• Abstract summary: Conservation laws and hydrodynamic transport can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R'enyi entropies. We introduce a class of long-range random Clifford circuits with U$(1)$ symmetry, which act as minimal models for more generic quantum systems. Our work sheds light on the interplay of transport and entanglement and emphasizes the usefulness of constrained Clifford circuits to explore questions in quantum many-body dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conservation laws and hydrodynamic transport can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R\'enyi entropies. Here, we introduce a class of long-range random Clifford circuits with U$(1)$ symmetry, which act as minimal models for more generic quantum systems and provide an ideal framework toexplore this phenomenon. Depending on the exponent $\alpha$ controlling the probability $\propto r^{-\alpha}$ of gates spanning a distance $r$, transport in such circuits varies from diffusive to superdiffusive and then to superballistic. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to $S(t) \propto t^{1/z}$, where $z$ is the $\alpha$-dependent dynamical transport exponent. We explain this finding in terms of the inhibited operator spreading in U$(1)$-symmetric Clifford circuits, where the emerging light cones are intimately related to the transport behavior and are significantly narrower compared to circuits without conservation law. For sufficiently small $\alpha$, we show that the presence of hydrodynamic modes becomes irrelevant such that $S(t)$ behaves similarly in circuits with and without conservation law. Our work sheds light on the interplay of transport and entanglement and emphasizes the usefulness of constrained Clifford circuits to explore questions in quantum many-body dynamics.

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