In the random-field XXZ model, Wehrl-Rényi entropy growth for z-polarized product states shows non-monotonic dependence on initial entanglement, with the first regime set by local integrals of motion and the second by inter-site correlations.
Local integrals of motion and the logarithmic lightcone in many-body localized systems
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abstract
We propose to define full many-body localization in terms of the recently introduced integrals of motion[Chandran et al., arXiv:1407.8480], which characterize the time-averaged response of the system to a local perturbation. The quasi-locality of such integrals of motion implies an effective lightcone that grows logarithmically in time. This subsequently implies that (i) the average entanglement entropy can grow at most logarithmically in time for a global quench from a product state, and (ii) with high probability, the time evolution of a local operator for a time interval $|t|$ can be classically simulated with a resource that scales polynomially in $|t|$.
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This review surveys the Loschmidt echo, OTOCs, and Krylov complexity as quantum proxies for classical Lyapunov exponents in chaotic systems.
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Entanglement Growth from Structured Initial States in Many-Body Localized Systems
In the random-field XXZ model, Wehrl-Rényi entropy growth for z-polarized product states shows non-monotonic dependence on initial entanglement, with the first regime set by local integrals of motion and the second by inter-site correlations.
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Quantum analogues of exponential sensitivity: from Loschmidt echo to Krylov complexity
This review surveys the Loschmidt echo, OTOCs, and Krylov complexity as quantum proxies for classical Lyapunov exponents in chaotic systems.