Comparing many-body localization lengths via non-perturbative construction of local integrals of motion
arXiv:1901.00034 · doi:10.1103/PhysRevB.100.214203
Abstract
Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum information. A phenomenological model, which describes the system using a complete set of local integrals of motion (LIOMs), provides a powerful tool to understand MBL, but can be usually only computed approximately. Here we explicitly compute a complete set of LIOMs with a non-perturbative approach, by maximizing the overlap between LIOMs and physical spin operators in real space. The set of LIOMs satisfies the desired exponential decay of weight of LIOMs in real-space. This LIOM construction enables a direct mapping from the real space Hamiltonian to the phenomenological model and thus enables studying the localized Hamiltonian and the system dynamics. We can thus study and compare the localization lengths extracted from the LIOM weights, their interactions, and dephasing dynamics, revealing interesting aspects of many-body localization. Our scheme is immune to accidental resonances and can be applied even at phase transition point, providing a novel tool to study the microscopic features of the phenomenological model of MBL.
arXiv comment8+3 pages, 8+6 figures
References in corpus (42)
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- 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 many-body localization phase transition
- Unbounded growth of entanglement in models of many-body localization
- Exploring the many-body localization transition in two dimensions
- Many body localization in Heisenberg XXZ magnet in a random field
- 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 in a quantum simulator with programmable random disorder
- On Many-Body Localization for Quantum Spin Chains
- Universal slow growth of entanglement in interacting strongly disordered systems
- Probing entanglement in a many-body-localized system
- Integrals of motion in the Many-Body localized phase
- Area laws in a many-body localized state and its implications for topological order
- Spectral signatures of many-body localization with interacting photons
- Coupling Identical 1D Many-Body Localized Systems
- Many-body localization in one dimension as a dynamical renormalization group fixed point
- Constructing local integrals of motion in the many-body localized phase
- Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
- Disorder-induced Localization in a Strongly Correlated Atomic Hubbard Gas
- Exploring Localization in Nuclear Spin Chains
- Quantum quenches in the many-body localized phase
- Interferometric probes of many-body localization
- Out-of-time-order correlations in many-body localized and thermal phases
- Explicit Local Integrals of Motion for the Many-Body Localized State
- Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
- Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization
- Engineering a flux-dependent mobility edge in disordered zigzag chains
- Quantum Mutual Information as a Probe for Many-Body Localization
- Fixed points of Wegner-Wilson flows and many-body localization
- Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
- Efficient representation of fully many-body localized systems using tensor networks
- Many-body localization and delocalization from the perspective of Integrals of Motion
- Explicit construction of local conserved operators in disordered many-body systems
- Emergent local integrals of motion without a complete set of localized eigenstates
- Construction of exact constants of motion and effective models for many-body localized systems
- Loschmidt Echo in Many-Body Localized Phase
- Approximating observables on eigenstates of large many-body localized systems
Cited by in corpus (15)
- Can we study the many-body localisation transition?
- Many-Body Localization in the Age of Classical Computing
- Numerical evidence for many-body localization in two and three dimensions
- Non-thermalized Dynamics of Flat-Band Many-Body Localization
- Extracting many body localization lengths with an imaginary vector potential
- Catching thermal avalanches in the disordered XXZ model
- Loschmidt echo singularities as dynamical signatures of strongly localized phases
- Spatio-temporal heterogeneity of entanglement in many-body localized systems
- Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
- Phenomenology of many-body localization in bond-disordered spin chains
- Probing localization properties of many-body Hamiltonians via an imaginary vector potential
- Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
- Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?
- Krylov complexity of many-body localization: Operator localization in Krylov basis
- Unified theory of local integrals of motion