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SUMMARY:Eigenstate Thermalization Hypothesis and Its Deviations from Rando
m-Matrix Theory beyond the Thermalization Time
DTSTART:20230525T120000Z
DTEND:20230525T133000Z
DTSTAMP:20240613T182300Z
UID:indico-event-42@indico.physik.uni-bielefeld.de
CONTACT:jschnack@uni-bielefeld.de
DESCRIPTION:Speakers: Jiaozi Wang\n\nThe eigenstate thermalization hypothe
sis explains the emergence of the thermodynamic equilibrium in isolated qu
antum many-body systems by assuming a particular structure of the observab
le’s matrix elements in the energy eigenbasis. Schematically\, it postul
ates that off-diagonal matrix elements are random numbers and the observab
les can be described by random matrix theory (RMT). To what extent a RMT d
escription applies\, more precisely at which energy scale matrix elements
of physical operators become truly uncorrelated\, is\, however\, not fully
understood. We study this issue by introducing a novel numerical approach
to probe correlations between matrix elements for Hilbert-space dimension
s beyond those accessible by exact diagonalization. Our analysis is based
on the evaluation of higher moments of operator submatrices\, defined with
in energy windows of varying width. Considering nonintegrable quantum spin
chains\, we observe that matrix elements remain correlated even for narro
w energy windows corresponding to timescales of the order of thermalizatio
n time of the respective observables. We also demonstrate that such residu
al correlations between matrix elements are reflected in the dynamics of o
ut-of-time-ordered correlation functions. Phys. Rev. Lett. 128\, 180601
(2022)\n\nhttps://indico.physik.uni-bielefeld.de/event/42/
LOCATION:D5-153 (UHG)
URL:https://indico.physik.uni-bielefeld.de/event/42/
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