Resistivity and its fluctuations in disordered many-body systems: From chains to planes

Abstract

We study a quantum particle coupled to hard-core bosons and propagating on disordered ladders with R legs. The particle dynamics is studied with the help of rate equations for the boson-assisted transitions between the Anderson states. We demonstrate that for finite R < ∞ and sufficiently strong disorder the dynamics is subdiffusive, while the two-dimensional planar systems with R → ∞ appear to be diffusive for arbitrarily strong disorder. The transition from diffusive to subdiffusive regimes may be identified via statistical fluctuations of resistivity. The corresponding distribution function in the diffusive regime has fat tails which decrease with the system size L much slower than 1/ √ L. Finally, we present evidence that similar non-Gaussian fluctuations arise also in standard models of many-body localization, i.e., in strongly disordered quantum spin chains.

Non-equilibrium boundary driven quantum systems: models, methods and properties

“…In (Iadecola and Žnidarič, 2019) the authors considered a spin ladder and showed that the presence of symmetries, independently of the strength of disorder, can be used to construct exponentially large subspaces which can be localized or ballistic. Another setup worth mentioning is that of a single particle in a lattice, with a disordered potential also coupled to a bosonic chain as in (Mierzejewski et al, 2019(Mierzejewski et al, , 2020Prelovšek et al, 2018). In this case the authors modeled the effect of the bosons on the single particle using Fermi golden rule to describe the transition between the eigenstates of the single particle Hamiltonian, and a rate equation to describe the injection and removal of particles at the edges of the system.…”

“…In one dimension, the authors of (Mierzejewski et al, 2019) find that strongly interacting bosons, in particular hardcore bosons, help the system to be subdiffusive, while more weakly interacting bosons can result in diffusive transport at long times. In (Mierzejewski et al, 2020) it is also shown that, while transport can be subdiffusive in one dimension, in two dimensions it would be diffusive, even for large disorder.…”

Ergodicity breaking transition in finite disordered spin chains

“…Our analysis applies to disorder averages of ergodicity indicators. When the disorder is increased, fluctuations of ergodicity indicators (at least in finite systems) may become anomalous, which has been observed in fluctuations of the entanglement entropy [45,[50][51][52][53] and in distributions of other observables [66,[113][114][115][116]. It remains open how the KT character of the transition of averaged quantities is related to other statistical properties of the model.…”

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

“…For stronger disorder, the toy model reveals an anomalous transport reported in several numerical studies [13,[43][44][45]. To explain its origin, in Fig.…”