Data of publication "Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems"
Authors/Creators
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1.
Osnabrück University
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2.
Leibniz University Hannover
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3.
University of Kentucky
Description
We study statistical properties of matrix elements entering the eigenstate thermalization hypoth-
esis by studying the observables written in the energy eigenbasis and truncated to small micro-
canonical windows. We put forward a picture, that below certain energy scale collective statistical
properties of matrix elements exhibit emergent unitary symmetry. In particular, below this scale the
spectrum of the microcanonically truncated operator exhibits universal behavior for which we intro-
duce readily testable criteria. We support this picture by numerical simulations and demonstrate
existence of emergent unitary symmetry scale for all considered operators in chaotic many-body
quantum systems. We discuss operator and system-size dependence of this energy scale and put our
findings into context of previous works exploring emergence of random-matrix behavior in narrow
energy windows.
Other (English)
This work has been funded by the
Deutsche Forschungsgemeinschaft (DFG), under Grant
No. 397107022, No. 397067869, and No. 397082825,
within the DFG Research Unit FOR 2692, under Grant
No. 355031190. A. D. is supported by the National
Science Foundation under Grant No. PHY 2310426.
This work was performed in part at Aspen Center for
Physics, which is supported by National Science Foun-
dation grant PHY-2210452. J. R. acknowledges funding
from the European Union’s Horizon Europe research and
innovation programme, Marie Sklodowska-Curie grant
no. 101060162, and the Packard Foundation through a
Packard Fellowship in Science and Engineering.
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- Is published in
- Publication: arXiv:2310.20264 (arXiv)