# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 9: Many-body Systems: Equilibration, Chaos and Localization I (joint session DY/TT)

### TT 9.8: Vortrag

### Montag, 16. März 2020, 12:00–12:15, HÜL 186

Statistics of correlations functions in the random Heisenberg chain — •Luis Colmenarez^{1}, David Luitz^{1}, Paul McClarty^{1}, and Masudul Haque^{1,2} — ^{1}Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, Dresden, Germany — ^{2}Department of Theoretical Physics, Maynooth University, Co. Kildare, Ireland

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. We consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. 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 S_{i}^{z}S_{i+r}^{z} 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 S_{i}^{z}S_{i+r}^{z} correlator exhibits striking differences between the MBL and Anderson insulator cases.