## SciPost Submission Page

# Statistics of correlations across the many-body localization transition

### by Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz

### 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.