Hilbert-space localization in closed quantum systems

Abstract

Quantum localization within an energy-shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space "Anderson localization" and its many-body Fock-space version. We use the term "Hilbert-space localization" in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the Bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state, and on the strength of the many-body interactions using a novel recursive projection method.

12 pages, 8 figures

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• Entanglement entropy, single-particle occupation probabilities, and short-range correlations
• Exploring many body localization and thermalization using semiclassical method
• Semiclassical theory of strong localization for quantum thermalization
• Randomly repeated measurements on quantum systems: Correlations and topological invariants of the quantum evolution
• Classical route to ergodicity and scarring in collective quantum systems
• Entanglement production by statistical operators
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Non-Markovian character and irreversibility of real-time quantum many-body dynamics
• Entanglement transition through Hilbert-space localization
• Probing many-body systems near spectral degeneracies
• Quantized dynamics in closed quantum systems
• Controlling dynamical entanglement in a Josephson tunneling junction