Gumbel statistics for entanglement spectra of many-body localized eigenstates

Abstract

An entanglement spectrum encodes statistics beyond the entanglement entropy, of which several have been studied in the context of many-body localization. We numerically study the extreme value statistics of entanglement spectra of many-body localized eigenstates. The physical information encoded in these spectra is almost fully carried by the few smallest elements, suggesting the extreme value statistics to have physical significance. We report the surprising observation of Gumbel statistics. Our result provides an analytical, parameter-free characterization of many-body localized eigenstates.

arXiv comment5 pages, 3 figures

References in corpus (39)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Average Entropy of a Subsystem
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Unbounded growth of entanglement in models of many-body localization
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Quantum entanglement in condensed matter systems
• Universal slow growth of entanglement in interacting strongly disordered systems
• Integrals of motion in the Many-Body localized phase
• The Ergodic Side of the Many-Body Localization Transition
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Probing quantum and thermal noise in an interacting many-body system
• Universal Fluctuations in Correlated Systems
• Critical Properties of the Many-Body Localization Transition
• Quantum quenches in the many-body localized phase
• Exact Maximal Height Distribution of Fluctuating Interfaces
• 1/f Noise and Extreme Value Statistics
• Many body localization and thermalization: insights from the entanglement spectrum
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Power-Law Entanglement Spectrum in Many-Body Localized Phases
• Two-component Structure in the Entanglement Spectrum of Highly Excited States
• Global fluctuations and Gumbel statistics
• Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
• Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Full counting statistics of time of flight images
• Renormalization group theory for finite-size scaling in extreme statistics
• Extreme statistics of complex random and quantum chaotic states
• Characterizing the many-body localization transition through the entanglement spectrum
• Universality-class dependence of energy distributions in spin glasses
• Entanglement critical length at the many-body localization transition

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• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Probing the randomness of ergodic states: extreme-value statistics in the ergodic and many-body-localized phases