While the high-temperature spin diffusion in spin chains with random local
fields has been the subject of numerous studies concerning the phenomenon of
many-body localization (MBL), the energy diffusion in the same models has been
much less explored. We show that energy diffusion is faster at weak random
fields but becomes essentially equal at strong fields; hence, both diffusions
determine the slowest relaxation time scale (Thouless time) in the system.
Numerically reachable finite-size systems reveal the anomalously large
distribution of diffusion constants with respect to actual field
configurations. Despite the exponential-like dependence of diffusion on field
strength, results for the sensitivity to twisted boundary conditions are
incompatible with the Thouless criterion for localization and the presumable
transition to MBL, at least for numerically reachable sizes. In contrast, we
find indications for the scenario of subdiffusive transport, in particular in
the dynamical diffusivity response.

Questo articolo esplora i giri e le loro implicazioni.

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