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

By B. Bertini, Pavel Kos, Tomaz Prosen. SciPost Physics, 2019

139 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a63ed4388b3d4fa36861b9bce3aaee78a88893bd

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In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. Tianci Zhou
6. B. Skinner
7. J. Ruhman
8. Nicholas Hunter-Jones

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. Tianci Zhou
5. S. Vijay
6. D. Huse
7. Nicholas Hunter-Jones
8. J. Ruhman

In Statistical and Nonlinear Physics

1. A. Nahum
2. Tianci Zhou
3. S. Vijay
4. Matthew Fisher
5. V. Khemani

Citations in the corpus

• Random Quantum Circuits (2022, background): “Various properties such as emergence of RMT spectral correlations in the SFF (210); the dynamics of state and operator entanglement (217, 216, 218, 219, 220, 221); unequal time correlation functions, both time-ordered and out-of-time-ordered (119, 186); and the eigenstate thermalization hypothesis (”
• Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “[49] Bruno Bertini, Pavel Kos, and Tomaž Prosen.”