Time Evolution of Many-Body Localized Systems with the Flow Equation Approach

Abstract

The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling this interesting regime, here we develop a semi-analytical flow equation approach to study time evolution of strongly disordered interacting quantum systems. We apply this technique to a prototype model of interacting spinless fermions in a random on-site potential in both one and two dimensions. Key results include (i) an explicit construction of the local integrals of motion that characterize the many-body localized phase in one dimension, ultimately connecting the microscopic model to phenomenological descriptions, (ii) calculation of these quantities for the first time in two dimensions, and (iii) an investigation of the real-time dynamics in the localized phase which reveals the crucial role of $l$-bit interactions for enhancing dephasing and relaxation.

5+5pages, 2+4 figures; Revised version, new results in d=2 added

References in corpus (25)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Many-body localization in periodically driven systems
• Integrals of motion in the Many-Body localized phase
• Interaction Quench in the Hubbard model
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Anomalous thermalization in ergodic systems
• Quantum quenches in the many-body localized phase
• Quantum revivals and many-body localization
• Possible experimental manifestations of the many-body localization
• Delocalized Glassy Dynamics and Many Body Localization
• Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
• Thermal inclusions: how one spin can destroy a many-body localized phase
• Unitary perturbation theory approach to real-time evolution problems
• The fate of dynamical many-body localization in the presence of disorder
• Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations
• Derivation of the t-J model for finite doping
• Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations
• Single spin probe of Many-Body Localization

Cited by in corpus (76)

• Many-body localization, thermalization, and entanglement
• Many-body localization: an introduction and selected topics
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Thouless time analysis of Anderson and many-body localization transitions
• Challenges to observation of many-body localization
• Polynomially filtered exact diagonalization approach to many-body localization
• Many-Body Localization in the Age of Classical Computing
• Shift-invert diagonalization of large many-body localizing spin chains
• Level statistics across the many--body localization transition
• Strong Disorder RG approach - a short review of recent developments
• Signatures of the Many-body Localized Regime in Two Dimensions
• Slow many-body delocalization beyond one dimension
• Solving efficiently the dynamics of many-body localized systems at strong disorder
• A flow equation approach to periodically driven quantum systems
• Are many-body localized systems stable in the presence of a small bath?
• Stability of many-body localization in Floquet systems
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• Universality in Anderson localization on random graphs with varying connectivity
• Behavior of l-bits near the many-body localization transition
• Construction of exact constants of motion and effective models for many-body localized systems
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows
• Many-body localization transition in large quantum spin chains: The mobility edge
• Hilbert-space fragmentation, multifractality, and many-body localization
• Numerical evidence for many-body localization in two and three dimensions
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• Many-body localization as a large family of localized ground states
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• Catching thermal avalanches in the disordered XXZ model
• Almost-conserved operators in nearly many-body localized systems
• Many-body delocalization from embedded thermal inclusion
• Describing many-body localized systems in thermal environments
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
• Dissipative flow equations
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Quantum quenches in isolated quantum glasses out of equilibrium
• Approximating observables on eigenstates of large many-body localized systems
• Many-Body Mobility Edge in Quantum Sun models
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models
• Flow Equations for Disordered Floquet Systems
• Many-body localization in one dimensional optical lattice with speckle disorder
• Nonstabilizerness dynamics in many-body localized systems
• Breaking the chains: extreme value statistics and localization in random spin chains
• Efficient flow equations for dissipative systems
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Measuring out quasi-local integrals of motion from entanglement
• Phenomenology of many-body localization in bond-disordered spin chains
• Unraveling long-time quantum dynamics using flow equations
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Fate of Algebraic Many-Body Localization under driving
• Construction of Many-Body Eigenstates with Displacement Transformations
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Edge mode locality in perturbed symmetry protected topological order
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
• Boosting entanglement growth of many-body localization by superpositions of disorder
• Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Renormalization view on resonance proliferation between many-body localized phases
• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Localization and interactions in topological and non-topological bands in two dimensions
• Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain