Colmenarez, Luis and McClarty, Paul A. and Haque, Masudul and Luitz, David J. (2019) Statistics of correlation functions in the random Heisenberg chain. SciPost Physics, 7 (064). ISSN 2542-4653

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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 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 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 SziSzi+r correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising 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 SziSzi+r correlator exhibits striking differences between the MBL and Anderson insulator cases.

Item Type:	Article
Additional Information:	Copyright L. Colmenarez et al. This work is licensed under the Creative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by/4.0/. Published by the SciPost Foundation. Cite as: Statistics of correlation functions in the random Heisenberg chain. Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz. SciPost Phys. 7, 064 (2019) · published 21 November 2019. DOI: 10.21468/SciPostPhys.7.5.064
Keywords:	correlation functions; random Heisenberg chain;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	14835
Identification Number:	https://doi.org/10.21468/SciPostPhys.7.5.064
Depositing User:	Masud Haque
Date Deposited:	17 Sep 2021 15:57
Journal or Publication Title:	SciPost Physics
Publisher:	SciPost
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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