# Statistics of correlations across the many-body localization transition

### Submission summary

 As Contributors: Luis A. Colmenarez Arxiv Link: https://arxiv.org/abs/1906.10701v2 Date submitted: 2019-07-17 Submitted by: Colmenarez, Luis A. Submitted to: SciPost Physics Domain(s): Theor. & Comp. Subject area: Quantum Physics

### Abstract

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of \emph{eigenstate correlation functions} across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for \emph{anomalous thermalization} in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A \emph{quantitative quasi-degenerate perturbation theory} calculation of these correlators yields a surprising \emph{agreement of the full distribution} with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1906.10701v2 on 17 July 2019