Universal spectral form factor for many-body localization

Abstract

We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body-localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.

arXiv comment(6+15) pages, (3+13) figures; close to published version

References in corpus (43)

• Chaos and Quantum Thermalization
• Many body localization and thermalization in quantum statistical mechanics
• 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
• Exploring the many-body localization transition in two dimensions
• 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
• Many-body localization in a quantum simulator with programmable random disorder
• The approach to thermal equilibrium in quantized chaotic systems
• Probing entanglement in a many-body-localized system
• Spectral signatures of many-body localization with interacting photons
• 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
• Thouless time analysis of Anderson and many-body localization transitions
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Spectral statistics across the many-body localization transition
• Critical Properties of the Many-Body Localization Transition
• Distinguishing localization from chaos: challenges in finite-size systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Can we study the many-body localisation transition?
• Many-body quantum chaos: Analytic connection to random matrix theory
• Onset of Random Matrix Behavior in Scrambling Systems
• Analytically solvable renormalization group for the many-body localization transition
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Symmetry constraints on many-body localization
• Spectral form factors and late time quantum chaos
• Level statistics across the many--body localization transition
• Many-body localization near the critical point
• Dynamics and Transport at the Threshold of Many-Body Localization
• Many-body localization in incommensurate models with a mobility edge
• Model of level statistics for disordered interacting quantum many-body systems
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Nonperturbative theory of power spectrum in complex systems
• Power spectrum and form factor in random diagonal matrices and integrable billiards

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• Many-body quantum chaos in stroboscopically-driven cold atoms
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors
• Isospectral twirling and quantum chaos
• Random Matrix Theory of the Isospectral twirling
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scale-invariant critical dynamics at eigenstate transitions
• Signatures of a critical point in the many-body localization transition
• Restoring ergodicity in a strongly disordered interacting chain
• Power spectrum and form factor in random diagonal matrices and integrable billiards
• Signatures of quantum chaos in low-energy mixtures of few fermions
• Exact universal bounds on quantum dynamics and fast scrambling
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Nonstabilizerness dynamics in many-body localized systems
• Unveiling Order from Chaos by approximate 2-localization of random matrices
• Single-Particle Universality of the Many-Body Spectral Form Factor
• Phenomenology of many-body localization in bond-disordered spin chains
• Quantum Chaos in Random Ising Networks
• Higher-order gap ratios of singular values in open quantum systems
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Spectral form factors and dynamical localization
• Long-ranged spectral correlations in eigenstate phases
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Transition to chaos in extended systems and their quantum impurity models
• Discrete time crystals detected by time-translation twist
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Signatures of quantum chaos and complexity in the Ising model on random graphs
• Lax random matrices from Calogero systems
• Crystalline Spectral Form Factors
• On the difference between thermalization in open and isolated quantum systems: a case study
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Thouless Energy Across Many-Body Localization Transition in Floquet Systems
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Many-body spectral transitions through the lens of the variable-range SYK2 model