Operator entanglement entropy of the time evolution operator in chaotic systems

Abstract

We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized and Floquet systems. In the random field Heisenberg model we find a universal power law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases. In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value). We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent-Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL and Floquet properties as the original Hamiltonian. The scaling and saturation properties reflect the spreading of the state EE of the corresponding time evolution. We conclude that the EE of the evolution operator should characterize the propagation of information in these systems.

18 pages, 14 figures. Revised version has added a refined argument and numerical evidence for the deficit value in the disordered Heisenberg model

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Operator space entanglement entropy in transverse Ising chain
• Anomalous thermalization in ergodic systems
• Operator Space Entanglement Entropy in XY Spin Chains
• A Floquet Model for the Many-Body Localization Transition
• Chaos and Complexity of quantum motion
• Thermalization of entanglement
• Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement
• Entangling power of quantum chaotic evolutions via operator entanglement

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• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Absence of dynamical localization in interacting driven systems
• Prethermal time crystals in a one-dimensional periodically driven Floquet system
• Random Matrix Theory of the Isospectral twirling
• Topological lower bound on quantum chaos by entanglement growth
• Purification and scrambling in a chaotic Hamiltonian dynamics with measurements
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Entanglement dynamics of thermofield double states in integrable models
• Response of a quantum disordered spin system to a local periodic drive