Dephasing in strongly disordered interacting quantum wires

Abstract

Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference, i.e., localization, with many-body interaction-induced dephasing. Numerous computational tests and also several experiments have been put forward to support the basic concept. Typically, averages of time-dependent global observables have been considered, such as the charge imbalance. We here investigate within the disordered spinless Hubbard ($t\text{\ensuremath{-}}V$) model how dephasing manifests in time-dependent variances of observables. We find that after quenching a N\'eel state the local charge density exhibits strong temporal fluctuations with a damping that is sensitive to disorder $W$: variances decay in a power-law manner, ${t}^{\ensuremath{-}\ensuremath{\zeta}}$, with an exponent $\ensuremath{\zeta}(W)$ strongly varying with $W$. A heuristic argument suggests the form $\ensuremath{\zeta}\ensuremath{\approx}\ensuremath{\alpha}(W){\ensuremath{\xi}}_{\text{sp}}$, where ${\ensuremath{\xi}}_{\text{sp}}(W)$ denotes the noninteracting localization length and $\ensuremath{\alpha}(W)$ characterizes the multifractal structure of the dynamically active volume fraction of the many-body Hilbert space. In order to elucidate correlations underlying the damping mechanism, exact computations are compared with results from the time-dependent Hartree-Fock approximation. Implications for experimentally relevant observables, such as the imbalance, will be discussed.