Dresden 2020 – wissenschaftliches Programm
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DY 5.8: Vortrag
Montag, 16. März 2020, 12:00–12:15, HÜL 186
Statistics of correlations functions in the random Heisenberg chain — •Luis Colmenarez1, David Luitz1, Paul McClarty1, and Masudul Haque1,2 — 1Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, Dresden, Germany — 2Department 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 SizSi+rz 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 SizSi+rz correlator exhibits striking differences between the MBL and Anderson insulator cases.