Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits

2019/09/16 by Bruno Bertini, Pavel Kos, Tomaz Prosen · 1 voice · 13 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.stat-mech #hep-th #nlin.CD #quant-ph

paper · pdf · doi:10.21468/scipostphys.8.4.067

openalex publication_date 2020/04/28 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

The entanglement in operator space is a well established measure for the complexity of quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study the dynamics of local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quantum circuits that we recently introduced. We identify a class of ``completely chaotic" dual-unitary circuits where the local-operator entanglement grows linearly and we provide a conjecture for its asymptotic behaviour which is in excellent agreement with the numerical results. Interestingly, our conjecture also predicts a ``phase transition" in the slope of the local-operator entanglement when varying the parameters of the circuits.

Citations

• Entanglement in many-body systems

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Discussions

• N.B: I've drawn the diagrams with the convention of time going 'up' the page, as opposed to the usual convention (in the QC literature) of time going from left to right, across the page. Sorry; this i [stackexchange, 5 points]

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