Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge

Abstract

We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of non-interacting fermions where the entanglement entropy manifests a volume law (`extended'), but there are large fluctuations in the subsystem particle numbers (`nonergodic'). We argue such an intermediate phase scenario may continue holding even for the many-body localization in the presence of interactions as well. We find for many-body states in non-interacting 1d Aubry-Andre and 3d Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is sub-thermal but obeys the "volume law". In the vicinity of the localization transition we find that both the entanglement entropy and the particle number fluctuations obey a single parameter scaling. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition eventually to the usual ergodic many-body extended phase.

23 pages, 19 figures, replaced with published version, Editors' Suggestion

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Cited by in corpus (91)

• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Observation of tunable mobility edges in generalized Aubry-André lattices
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• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Extended nonergodic states in disordered many-body quantum systems
• Many-body critical phase: extended and nonthermal
• Universal properties of many-body localization transitions in quasiperiodic systems
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Anderson localization transitions with and without random potentials
• Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Many-body localization in incommensurate models with a mobility edge
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Quantum phase with coexisting localized, extended, and critical zones
• Logarithmic Entanglement Lightcone in Many-Body Localized Systems
• Quasiperiodic quantum heat engines with a mobility edge
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Eigenstate Gibbs Ensemble in Integrable Quantum Systems
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
• Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential
• Many-body localization in presence of cavity mediated long-range interactions
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• Dynamical many-body localization in an integrable model
• Dynamical localization and the effects of aperiodicity in Floquet systems
• Non-Hermitian skin effects on many-body localized and thermal phases
• Multifractality and self-averaging at the many-body localization transition
• Novel mobility edges in the off-diagonal disordered tight-binding models
• Investigating many-body mobility edges in isolated quantum systems
• Transport in Stark Many Body Localized Systems
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Edge and bulk localization of Floquet topological superconductors
• Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model
• Detecting delocalization-localization transitions from full density distributions
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Statistical Bubble Localization with Random Interactions
• Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
• Classifying transport behavior via current fluctuations in open quantum systems
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Configuration-Controlled Many-Body Localization and the Mobility Emulsion
• A numerical study of the localization transition of Aubry-André type models
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Interaction-enhanced many body localization in a generalized Aubry-Andre model
• Localization and topological transitions in generalized non-Hermitian SSH models
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
• Hidden thermal structure in Fock space
• Non-Abelian gauge potential driven localization transition in quasiperiodic optical lattices
• Absence of Many-Body Localization in a Single Landau Level
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Characterizing The Many-Body Localization via Studying State Sensitivity to Boundary Conditions
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Open-system eigenstate thermalization in a noninteracting integrable model
• Characterization of many-body mobility edges with random matrices
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Long-ranged spectral correlations in eigenstate phases
• Breakdown of Landau Fermi liquid theory: restrictions on the degrees of freedom of quantum electrons
• Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Interacting quasiperiodic spin chains in the prethermal regime
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Critical quantum dynamics of observables at eigenstate transitions
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Unsupervised machine learning for detecting mutual independence among eigenstate regimes in interacting quasiperiodic chains
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
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• Many-body localization in a slowly varying potential
• Dephasing-enhanced performance in quasiperiodic thermal machines
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• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions