Energy level correlations in a disordered one-dimensional chain

Niaz Ali Khan

Radu Pitiş, P. Gärtner

Transport on a one-dimensional nonuniform periodic chain with a hard-core interaction is examined. The mean-field conductivity is rederived, and the first correction due to many-particle effects is obtained. By letting the period go to infinity, the results are extended to nonperiodic chains, including the random one. The case of the site-disordered system with two values of the site energy is discussed in detail.

M. Ya. Mints

Jonas Richter, Dennis Schubert, Robin Steinigeweg

The real-time dynamics of equal-site correlation functions is studied for one-dimensional spin models with quenched disorder.Focusing on infinite temperature, we present a comparison between the dynamics of models with different quantum numbers S = 1 2 , 1, 3 2 , as well as of chains consisting of classical spins.Based on this comparison as well as by analyzing the statistics of energy-level spacings, we show that the putative many-body localization transition is shifted to considerably stronger values of disorder for increasing S. In this context, we introduce an effective disorder strength W eff , which provides a mapping between the dynamics for different spin quantum numbers.For small W eff , we show that the real-time correlations become essentially independent of S, and are moreover very well captured by the dynamics of classical spins.Especially for S = 3 2 , the agreement between quantum and classical dynamics is remarkably observed even for very strong values of disorder.This behavior also reflects itself in the corresponding spectral functions, which are obtained via a Fourier transform from the time to the frequency domain.As an aside, we also comment on the self-averaging properties of the correlation function at weak and strong disorder.Our work sheds light on the correspondence between quantum and classical dynamics at high temperatures and extends our understanding of the dynamics in disordered spin chains beyond the well-studied case of S = 1 2 .

Corentin Bertrand, Antonio M. Garcı́a-Garcı́a

We study a one-dimensional XXZ spin chain in a random field on the metallic side of the many-body localization transition by level statistics. For a fixed interaction, and intermediate disorder below the many-body localization transition, we find that, asymptotically, the number variance grows faster than linear with a disorder-dependent exponent. This is consistent with the existence of an anomalous Thouless energy in the spectrum. In noninteracting disordered metals, this is an energy scale related to the typical time for a particle to diffuse across the sample. In the interacting case, it seems related to a more intricate anomalous diffusion process. This interpretation is not fully consistent with recent claims that for intermediate disorder, level statistics are described by a plasma model with power-law decaying interactions whose number variance grows slower than linear. As disorder is further increased, still on the metallic side, the Thouless energy is gradually washed out. In the range of sizes we can explore, level statistics are scale invariant and approach Poisson statistics at the many-body localization transition. Slightly below the many-body localization transition, spectral correlations, well described by critical statistics, are quantitatively similar to those of a high-dimensional, noninteracting, disordered conductor at the Anderson transition.

Daniel I. Khomskii