We investigate charge relaxation in quantum wires of spinless disordered fermions (t-V model). Our observable is the time-dependent density propagator Π_{ϵ}(x,t), calculated in windows of different energy density ϵ of the many-body Hamiltonian and at different disorder strengths W, not exceeding the critical value W_{c}. The width Δx_{ϵ}(t) of Π_{ϵ}(x,t) exhibits a behavior dlnΔx_{ϵ}(t)/dlnt=β_{ϵ}(t), where the exponent function β_{ϵ}(t)≲1/2 is seen to depend strongly on L at all investigated parameter combinations. (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that β_{ϵ}(t)<1/2 in a large window of times. However, subdiffusion might possibly be transient, only, finally giving way to a conventional diffusive behavior with β_{ϵ}=1/2. (ii) We cannot confirm the existence of many-body mobility edges even in regions of the phase diagram that have been reported to be deep in the delocalized phase. (iii) (Transient) subdiffusion 0<β_{ϵ}(t)≲1/2 coexists with an enhanced probability for returning to the origin Π_{ϵ}(0,t), decaying much slower than 1/Δx_{ϵ}(t). Correspondingly, the spatial decay of Π_{ϵ}(x,t) is far from Gaussian, being exponential or even slower. On a phenomenological level, our findings are broadly consistent with the effects of strong disorder and (fractal) Griffiths regions.

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The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modelling the time evolution as cellular automata for specific cases of dipole-and quadrupole-conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher moment conservation.

We demonstrate that the quantum mutual information (QMI) is a useful probe to study manybody localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from an MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

We study the t−V disordered spinless fermionic chain in the strong coupling regime, t/V → 0. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion. arXiv:1909.03073v1 [cond-mat.dis-nn]