Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos

By B. Bertini, Pavel Kos, Tomaz Prosen. Physical Review X, 2018

217 citations recorded by the source corpus.

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of “maximally chaotic,” periodically driven, quantum spin chains. Specifically, we consider the so-called “self-dual” kicked Ising chains initialized in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the maximally chaotic models considered: Their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so-called “minimal cut” bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel “duality-based” numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is nonintegrable.

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

View Paper: https://www.semanticscholar.org/paper/785bdb551fabacbfa3b550e610fcdd467a1051c4

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Citations in the corpus

Random Quantum Circuits (2022, methodology): “Apart from the limit of infinite q mentioned above, direct calculations of the von Neumann entropy have so far been possible only for circuits with special structure such as dual unitarity (161) (Sec.”
Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “We also investigate a special case of the kicked Ising model that has maximal entanglement growth [35, 36] and the property of “dual unitarity” which, remarkably, allows a range of exact computations [36, 46–49].”
Unitary circuits of finite depth and infinite width from quantum channels (2019, methodology): “[20] Bruno Bertini, Pavel Kos, and Tomaz Prosen, “Entanglement spreading in a minimal model of maximal manybody quantum chaos,” (2018), arXiv:1812.”
Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “As for unitary Hamiltonian dynamics, there is a notion of chaos in such Floquet circuits, as diagnosed by the entanglement growth [49, 50], the operator growth (and butterfly effect in out-of-time-order correlator) [51], the level spacing statistics and the spectral form factor [45, 46, 48, 52], etc”
Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits (2019, background): “While in the previous subsections we showed that this can be done for the completely chaotic subclass, here we show that the limits can be computed exactly also in the paradigmatic example of dual-unitary circuits in d = 2: the self-dual kicked Ising model [57, 58].”