Phenomenology of spectral functions in disordered spin chains at infinite temperature

Abstract

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

References in corpus (76)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• 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: an introduction and selected topics
• On Many-Body Localization for Quantum Spin Chains
• Eigenstate Thermalization Hypothesis
• Universal dynamics and renormalization in many body localized systems
• Integrals of motion in the Many-Body localized phase
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Quantum chaos challenges many-body localization
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• 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
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Multifractal Scalings across the Many-Body Localization Transition
• Remarks on the notion of quantum integrability
• Ergodicity breaking in a model showing many-body localization
• Finite-size scaling of eigenstate thermalization
• Many-body localization characterized from a one-particle perspective
• Thouless time analysis of Anderson and many-body localization transitions
• Rare region effects and dynamics near the many-body localization transition
• Dynamical obstruction to localization in a disordered spin chain
• Distinguishing localization from chaos: challenges in finite-size systems
• Anomalous thermalization in ergodic systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Can we study the many-body localisation transition?
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Thouless energy and multifractality across the many-body localization transition
• Polynomially filtered exact diagonalization approach to many-body localization
• Absence of true localization in many-body localized phases
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Thouless and relaxation time scales in many-body quantum systems
• Entanglement and matrix elements of observables in interacting integrable systems
• Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Time dynamics with matrix product states: Many-body localization transition of large systems revisited
• Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Fock-space correlations and the origins of many-body localisation
• Noise-induced subdiffusion in strongly localized quantum systems
• Eigenstate thermalization hypothesis and integrals of motion
• Many-body localization in Fock-space: a local perspective
• Solving efficiently the dynamics of many-body localized systems at strong disorder
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
• Universal dynamics of density correlations at the transition to many-body localized state
• Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows
• Self-consistent approach to many-body localization and subdiffusion
• Signatures of a critical point in the many-body localization transition
• Transient and persistent particle subdiffusion in a disordered chain coupled to bosons
• Many-body localization as a percolation phenomenon
• Einstein relation for a driven disordered quantum chain in subdiffusive regime

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• Challenges to observation of many-body localization
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• Phenomenology of the Prethermal Many-Body Localized Regime
• Stability of many-body localization in Floquet systems
• Universality in Anderson localization on random graphs with varying connectivity
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Restoring ergodicity in a strongly disordered interacting chain
• Fractal nature of high-order time crystal phases
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• Many-body localization and the area law in two dimensions
• Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Strongly disordered Anderson insulator chains with generic two-body interaction
• Fermionic Magic Resources of Quantum Many-Body Systems
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Reviving product states in the disordered Heisenberg chain
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Quantum logarithmic multifractality
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Disorder effects in the ${\mathbb{Z}}_3$ Fock parafermion chain
• Interacting quasiperiodic spin chains in the prethermal regime
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Ergodicity breaking transition in zero dimensions
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Tunable Hilbert space fragmentation and extended critical regime
• Relaxation mechanisms in a disordered system with the Poisson level statistics
• Information Bounds on phase transitions in disordered systems