Self-consistent approach to many-body localization and subdiffusion

Abstract

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization. Results show a qualitative agreement with numerically obtained dynamical structure factor in the whole range of frequencies and wavevectors, as well as across the transition to the nonergodic behavior. The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity $\sigma (\omega )\propto |\omega {|}^{\alpha }$, i.e., with vanishing d.c. limit ${\sigma }_0=0$ and $\alpha <1$ varying with disorder, while we get $\alpha >1$ in the localized phase.

References in corpus (15)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Phenomenology of fully many-body-localized systems
• 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
• The Ergodic Side of the Many-Body Localization Transition
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Ergodicity breaking in a model showing many-body localization
• Quantum quenches in the many-body localized phase
• Quantum revivals and many-body localization
• Absence of full many-body localization in the disordered Hubbard chain
• Finite temperature transport in disordered Heisenberg chains
• Density correlations and transport in models of many-body localization
• Universal dynamics of density correlations at the transition to many-body localized state
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain

Cited by in corpus (32)

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• Sub-diffusion in the Anderson model on random regular graph
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• Counting local integrals of motion in disordered spinless-fermion and Hubbard chains
• Spin subdiffusion in disordered Hubbard chain
• Many-body localization caused by temporal disorder
• Density correlations and transport in models of many-body localization
• Diffusive transport in a quasiperiodic Fibonacci chain: absence of many-body localization at small interactions
• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Phenomenology of anomalous transport in disordered one-dimensional systems
• Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain
• Many-body localization in XY spin chains with long-range interactions: An exact diagonalization study
• Reduced-basis approach to many-body localization
• Restoring ergodicity in a strongly disordered interacting chain
• Transient and persistent particle subdiffusion in a disordered chain coupled to bosons
• Many-body localization transition in a frustrated XY chain
• Relaxation at different length-scales in models of many-body localization
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Einstein relation for a driven disordered quantum chain in subdiffusive regime
• Multiple relaxation times in perturbed XXZ chain
• Boltzmann transport theory for many body localization
• Resistivity and its fluctuations in disordered many-body systems: from chains to planes
• Open-system spin transport and operator weight dissipation in spin chains
• Many-body localization of 1D disordered impenetrable two-component fermions
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Disordered impenetrable two-component fermions in one dimension