Probing Many-Body Quantum Chaos with Quantum Simulators
Abstract
The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified test bed to probe many-body quantum chaotic behavior, thermalization, and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin systems.
Additional Information
© 2022 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 5 July 2021; revised 13 October 2021; accepted 1 December 2021; published 27 January 2022) We thank Mikhail Baranov, Amos Chan, Manoj K. Joshi, Barbara Kraus, Rohan Poojary, Lukas Sieberer, and Denis Vasilyev for valuable discussions. Work in Innsbruck has been supported by the European Union's Horizon 2020 research and innovation program under Grant Agreements No. 817482 (Pasquans) and No. 731473 (QuantERA via QT-FLAG), by the Austrian Science Foundation (FWF, P 32597 N), by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, P. Z.), and by LASCEM by AFOSR No. 64896-PH-QC. A. E. acknowledges funding by the German National Academy of Sciences Leopoldina under Grant No. LPDS 2021-02. B. V. acknowledges funding from the French National Research Agency (ANR-20-CE47-0005, JCJC project QRand). A. V. and V. G. were supported by U.S.-ARO Contract No. W911NF1310172, NSF DMR-2037158, and the Simons Foundation.Attached Files
Published - PhysRevX.12.011018.pdf
Accepted Version - 2106.15530.pdf
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Additional details
- Eprint ID
- 113316
- Resolver ID
- CaltechAUTHORS:20220207-90373000
- 817482
- European Research Council (ERC)
- 731473
- European Research Council (ERC)
- P 32597 N
- FWF Der Wissenschaftsfonds
- 651440
- Simons Foundation
- 64896-PH-QC
- Air Force Office of Scientific Research (AFOSR)
- LPDS 2021-02
- Deutsche Akademie der Naturforscher Leopoldina
- ANR-20-CE47-0005
- Agence Nationale pour la Recherche (ANR)
- W911NF1310172
- Army Research Office (ARO)
- DMR-2037158
- NSF
- Created
-
2022-02-08Created from EPrint's datestamp field
- Updated
-
2022-02-08Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics