Many-body localization edge in the random-field Heisenberg chain
arXiv:1411.0660 · doi:10.1103/PhysRevB.91.081103
Abstract
We present a large scale exact diagonalization study of the one dimensional spin Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement and non ergodicity in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence.
4+3 pages, 5+3 figures
References in corpus (14)
- Thermalization and its mechanism for generic isolated quantum systems
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- Integrals of motion in the Many-Body localized phase
- Many-Body Localization in a Quasiperiodic System
- Ergodicity breaking in a model showing many-body localization
- Interferometric probes of many-body localization
- Many-body mobility edge in a mean-field quantum spin glass
- Quantum Quenches, Thermalization and Many-Body Localization
- Entanglement spreading in a many-body localized system
- Purification and many-body localization in cold atomic gases
- Participation spectroscopy and entanglement Hamiltonian of quantum spin models
Cited by in corpus (55)
- Spectral signatures of many-body localization with interacting photons
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Recent progress in many-body localization
- Anomalous thermalization in ergodic systems
- Many-body localization dynamics from gauge invariance
- How a small quantum bath can thermalize long localized chains
- Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
- Operator entanglement entropy of the time evolution operator in chaotic systems
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Many-body localization due to random interactions
- A Floquet Model for the Many-Body Localization Transition
- Quantum Mutual Information as a Probe for Many-Body Localization
- Extended nonergodic states in disordered many-body quantum systems
- Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
- Many-body localization in infinite chains
- Absence of full many-body localization in the disordered Hubbard chain
- Multifractality of wave functions on a Cayley tree: From root to leaves
- Transport properties across the many-body localization transition in quasiperiodic and random systems
- Full counting statistics in the Haldane-Shastry chain
- Explicit construction of local conserved operators in disordered many-body systems
- Prethermal time crystals in a one-dimensional periodically driven Floquet system
- A semi-classical limit for the many-body localization transition
- Clustering of non-ergodic eigenstates in quantum spin glasses
- Full counting statistics of the subsystem energy in the free fermions and the quantum spin chains
- Logarithmic Entanglement Lightcone in Many-Body Localized Systems
- Many-body localization caused by temporal disorder
- Emergent local integrals of motion without a complete set of localized eigenstates
- Universal dynamics of density correlations at the transition to many-body localized state
- Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
- Dynamics of quantum information in many-body localized systems
- Many-body localization for randomly interacting bosons
- Dynamics of many-body localization in the presence of particle loss
- Quantum and classical dynamics of a three-mode absorption refrigerator
- Many-body localization in Ising models with random long-range interactions
- Inverse participation ratios in the XXZ spin chain
- Statistical Bubble Localization with Random Interactions
- Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
- Many-body localization phase in a spin-driven chiral multiferroic chain
- Many-body localization of spinless fermions with attractive interactions in one dimension
- Eigenstate phases with finite on-site non-Abelian symmetry
- Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
- Nonequilibrium photonic transport and phase transition in an array of optical cavities
- Complete many-body localization in the t-J model caused by random magnetic field
- Many-Body-Localization Transition : sensitivity to twisted boundary conditions
- Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems
- Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
- On the quantum spin glass transition on the Bethe lattice
- Universal crossover from ground state to excited-state quantum criticality
- Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
- Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
- Many-body delocalization with random vector potentials
- Absence of Many-Body Localization in a Single Landau Level
- Many-body localization with mobility edges
- Multipoint entanglement in disordered systems
- Asymptotic Localization in the Bose-Hubbard Model