Many-Body Localization: Transitions in Spin Models

Abstract

We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths $1/2$ and $1$ are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance $({\Delta }_{s}r{)}^2$ of the averaged consecutive-gap ratio $⟨r⟩$ for different disorder realizations. For both types of systems and spin lengths we find a maximum in ${\Delta }_{s}r$ as a function of disorder strength, accompanied by an inflection point of $⟨r⟩$, signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.

arXiv comment11 pages, 9 figures. Comments welcome

References in corpus (49)

• Chaos and Quantum Thermalization
• Many body localization and thermalization in quantum statistical mechanics
• Random Matrix Theories in Quantum Physics: Common Concepts
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• 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
• On the phase structure of driven quantum systems
• Universal dynamics and renormalization in many body localized systems
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Quantum chaos challenges many-body localization
• Recent progress in many-body localization
• Extended slow dynamical regime close to the many-body localization transition
• The Ergodic Side of the Many-Body Localization Transition
• Constructing local integrals of motion in the many-body localized phase
• Emulating many-body localization with a superconducting quantum processor
• Two universality classes for the many-body localization transition
• Review: Local Integrals of Motion in Many-Body Localized systems
• Rare region effects and dynamics near the many-body localization transition
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Many-body localization and delocalization in large quantum chains
• Can we study the many-body localisation transition?
• Anderson localization on random regular graphs
• Early breakdown of area-law entanglement at many-body delocalization transition
• Polynomially filtered exact diagonalization approach to many-body localization
• Many body localization and thermalization: insights from the entanglement spectrum
• Observation of energy resolved many-body localization
• Long tail distributions near the many body localization transition
• Power-Law Entanglement Spectrum in Many-Body Localized Phases
• Entanglement versus chaos in disordered spin chains
• Time dynamics with matrix product states: Many-body localization transition of large systems revisited
• Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
• Many-body localization in infinite chains
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Lyapunov growth in quantum spin chains
• Many-body localization and mobility edge in a disordered Heisenberg spin ladder
• Characterizing the many-body localization transition through the entanglement spectrum
• Many-body localization transition in large quantum spin chains: The mobility edge
• Exploring many body localization and thermalization using semiclassical method
• Detection and characterization of Many-Body Localization in Central Spin Models
• Dynamical Many-body Localization and Delocalization in Periodically Driven Closed Quantum Systems
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Different types of integrability and their relation to decoherence in central spin models
• Many-body localization transition through pairwise correlations
• Studying many-body localization in exchange-coupled electron spin qubits using spin-spin correlations
• Quantum Coherence in Ergodic and Many-Body Localized Systems

Cited by in corpus (7)

• Many-Body Localization in the Age of Classical Computing
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Restoring ergodicity in a strongly disordered interacting chain
• Robustness of Stark many-body localization in the $J_1$-$J_2$ Heisenberg model
• Time-crystalline behavior in central-spin models with Heisenberg interactions
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains