Slow diffusion and Thouless localization criterion in modulated spin chains

Abstract

In recent years the ergodicity of disordered spin chains has been investigated via extensive numerical studies of the level statistics or the transport properties. However, a clear relationship between these results has yet to be established. We present the relation between the diffusion constant and the energy-level structure, which leads to the Thouless localization criterion. Together with the exponential-like dependence of the diffusion constant on the strength of quasiperiodic or random fields, the Thouless criterion explains the nearly linear drift with the system size of the crossover/transition to the nonergodic regime. Moreover, we show that the Heisenberg spin chain in the presence of the quasiperiodic fields can be well approached via a sequence of simple periodic systems, where diffusion remains finite even at large fields.

References in corpus (17)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• 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
• Many-Body Localization in a Quasiperiodic System
• 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
• Anomalous thermalization in ergodic systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Can we study the many-body localisation transition?
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Finite temperature transport in disordered Heisenberg chains
• Universal dynamics of density correlations at the transition to many-body localized state
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Spin diffusion and spin conductivity in the 2d Hubbard model

Cited by in corpus (9)

• Many-Body Localization in the Age of Classical Computing
• Emergent dipole moment conservation and subdiffusion in tilted chains
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Local integrals of motion in dipole-conserving models with Hilbert space fragmentation
• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Long-range resonances in quasiperiodic many-body localization
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain