Long-ranged spectral correlations in eigenstate phases
arXiv:2207.08454 · doi:10.1088/1751-8121/ad1342
Abstract
We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.
arXiv comment30 pages, 12 figures, 7 tables (including appendix), v2: minor corrections, improved presentation, close to published version
References in corpus (61)
- Chaos and Quantum Thermalization
- Many body localization and thermalization in quantum statistical mechanics
- A bound on chaos
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Exploring the many-body localization transition in two dimensions
- Many-body localization in a quantum simulator with programmable random disorder
- Operator Spreading in Random Unitary Circuits
- On Many-Body Localization for Quantum Spin Chains
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Probing entanglement in a many-body-localized system
- Spectral signatures of many-body localization with interacting photons
- Localization protected quantum order
- Many-Body Localization in a Quasiperiodic System
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Quantum chaos challenges many-body localization
- Stability and instability towards delocalization in MBL systems
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Exploring Localization in Nuclear Spin Chains
- Emulating many-body localization with a superconducting quantum processor
- Chaos, Complexity, and Random Matrices
- Two universality classes for the many-body localization transition
- Review: Local Integrals of Motion in Many-Body Localized systems
- Spectral statistics across the many-body localization transition
- Critical Properties of the Many-Body Localization Transition
- Ergodicity Breaking Transition in Finite Disordered Spin Chains
- Many-body quantum chaos: Analytic connection to random matrix theory
- Onset of Random Matrix Behavior in Scrambling Systems
- Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
- Spectral form factors and late time quantum chaos
- A Floquet Model for the Many-Body Localization Transition
- Quantum criticality of hot random spin chains
- Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
- Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
- Level statistics across the many--body localization transition
- Interaction instability of localization in quasiperiodic systems
- Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
- Many-Body Localization: Stability and Instability
- Dynamics and Transport at the Threshold of Many-Body Localization
- Transport properties across the many-body localization transition in quasiperiodic and random systems
- Many-body delocalisation as symmetry breaking
- Model of level statistics for disordered interacting quantum many-body systems
- Many-body localization in incommensurate models with a mobility edge
- Random Matrix Ensemble for the Level Statistics of Many-Body Localization
- Eigenstate phase transitions and the emergence of universal dynamics in highly excited states
- Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
- Universal spectral form factor for many-body localization
- Local resonances and parametric level dynamics in the many-body localised phase
- Universality and Quantum Criticality in Quasiperiodic Spin Chains
- Localization and symmetry breaking in the quantum quasiperiodic Ising glass
- Energy level statistics of the two-dimensional Hubbard model at low filling
- Many-body quantum chaos in stroboscopically-driven cold atoms
- Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
- Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model
- Nonperturbative theory of power spectrum in complex systems
- Eigenstate phases with finite on-site non-Abelian symmetry
- Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models
- Power spectrum and form factor in random diagonal matrices and integrable billiards
- Generalized Survival Probability