Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay

Soumya Bera; Giuseppe De Tomasi; Felix Weiner; Ferdinand Evers

doi:10.1103/PhysRevLett.118.196801

paper

Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay

arXiv:1610.03085 · doi:10.1103/PhysRevLett.118.196801

Abstract

We investigate charge relaxation in quantum-wires of spin-less 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 $Δ x_{ε} (t)$ of $Π_{ε} (x, t)$ exhibits a behavior $d ln Δ x_{ε} (t) / d ln t = β_{ε} (t)$ , 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 $β_{ε} < 1/2$ in 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 $1/Δ x_{ε} (t)$ . 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 effects of strong disorder and (fractal) Griffiths regions.

arXiv comment5+6 pages, 3+7 figures

Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay

Abstract

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