On the structure of typical states of a disordered Richardson model and many-body localization

Abstract

We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the delocalized phase which extends over the whole range of coupling strength in the thermodynamic limit. We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.

8 pages; references and figures added, last section expanded

References in corpus (8)

• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• Many body localization in Heisenberg XXZ magnet in a random field
• Remarks on the notion of quantum integrability
• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
• Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures
• Solving the Richardson equations close to the critical points

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• Many-body mobility edge in a mean-field quantum spin glass
• Many-Body Localization in the Age of Classical Computing
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Quantum Disentangled Liquids
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• The forward approximation as a mean field approximation for the Anderson and Many Body Localization transitions
• Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models
• Many-body localization and quantum ergodicity in disordered long-range Ising models
• Spin decoherence due to a randomly fluctuating spin bath
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• Signatures of many-body localisation in the dynamics of two-sites entanglement
• Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs
• Quantum annealing: the fastest route to quantum computation?
• Emergent fractal phase in energy stratified random models
• Engineering random spin models with atoms in a high-finesse cavity
• A Dirty Holographic Superconductor
• The quench action approach in finite integrable spin chains
• On the determinant representations of Gaudin models' scalar products and form factors
• Integrable spin chains with random interactions
• Dynamic nuclear polarization and the paradox of Quantum Thermalization
• Statistics of phase space localization measures and quantum chaos in the kicked top model
• Holographic p-wave Superconductor with Disorder
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• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Localization of disordered bosons and magnets in random fields
• Ergodic and localized regions in quantum spin glasses on the Bethe lattice
• Estimation of entanglement in bipartite systems directly from tomograms
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• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Multipoint entanglement in disordered systems
• A journey into localization, integrability and thermalization