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Register a new userAsymmetry in energy versus spin transport in certain interacting, disordered systems
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We study energy transport in XXZ spin chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries. We discuss the transition between diffusive and subdiffusive transport regimes in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder strengths. However, when finite magnetization is induced, both energy and spin currents decay as a function of system size with the same exponent. Based on this, we conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase-space; we suggest this is due to conservation laws present in the clean XXZ limit.
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Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, $r^{-alpha}$ with distance and $alpha<2$. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for $alpha>3/2$ the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.
We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can be distinguished by the scaling of the average resistance with the systems length. We address the following question: what is the distribution of resistance over different disorder realizations, and how does it differ between transport types? In particular, an often evoked so-called Griffiths picture, that aims to explain slow transport as being due to rare regions of high disorder, would predict that the diverging resistivity is due to fat power-law tails in the resistance distribution. Studying many-particle systems with and without interactions we do not find any clear signs of fat tails. The data is compatible with distributions that decay faster than any power law required by the fat tails scenario. Among the distributions compatible with the data, a simple additivity argument suggests a Gaussian distribution for a fractional power of the resistance.
We investigate the transition induced by disorder in a periodically-driven one-dimensional model displaying quantized topological transport. We show that, while instantaneous eigenstates are necessarily Anderson localized, the periodic driving plays a fundamental role in delocalizing Floquet states over the whole system, henceforth allowing for a steady state nearly-quantized current. Remarkably, this is linked to a localization/delocalization transition in the Floquet states of a one dimensional driven Anderson insulator, which occurs for periodic driving corresponding to a nontrivial loop in the parameter space. As a consequence, the Floquet spectrum becomes continuous in the delocalized phase, in contrast with a pure-point instantaneous spectrum.
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 spin-less Hubbard ($t-V$) model how dephasing manifests in time dependent variances of observables. We find that after quenching a Neel 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, $t^{-zeta}$, with an exponent $zeta(W)$ strongly varying with $W$. A heuristic argument suggests the form, $zetaapproxalpha(W)xi_text{sp}$, where $xi_text{sp}(W)$ denotes the noninteracting localization length and $alpha(W)$ 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.
We study the disordered Heisenberg spin chain, which exhibits many body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as $C sim t^{-beta}$, while the conductivity exhibits a low frequency power law $sigma sim omega^{alpha}$. The exponents depict sub-diffusive behavior $ beta < 1/2, alpha> 0 $ at all finite disorders, and convergence to the scaling result, $alpha+2beta = 1$, at large disorders.
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