Relaxation at different length-scales in models of many-body localization

Abstract

We study dynamical correlation functions in the random-field Heisenberg chain, which probes the relaxation times at different length scales. Firstly, we show that the relaxation time associated with the dynamical imbalance (examining the relaxation at the smallest length scale) decreases with disorder much faster than the one determined by the dc conductivity (probing the global response of the system). We argue that the observed dependence of relaxation on the length scale originates from local nonresonant regions. The latter have particularly long relaxation times or remain frozen, allowing for nonzero dc transport via higher-order processes. Based on the numerical evidence, we introduce a toy model that suggests that the nonresonant regions asymptotic dynamics are essential for the proper understanding of the disordered chains with many-body interactions.

References in corpus (13)

• 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
• 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
• Can we study the many-body localisation transition?
• Finite temperature transport in disordered Heisenberg chains
• Percolation in Fock space as a proxy for many-body localisation
• Universal dynamics of density correlations at the transition to many-body localized state
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models

Cited by in corpus (9)

• Many-Body Localization in the Age of Classical Computing
• Emergent dipole moment conservation and subdiffusion in tilted chains
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Tracking locality in time evolution of disordered systems
• Ergodicity breaking transition in zero dimensions
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Relaxation mechanisms in a disordered system with the Poisson level statistics