Journal
PHYSICAL REVIEW X
Volume 12, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.12.011018
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Funding
- European Union's Horizon 2020 research and innovation program [817482, 731473]
- Austrian Science Foundation (FWF) [P 32597 N]
- Simons Foundation [651440]
- LASCEM by AFOSR [64896-PH-QC]
- German National Academy of Sciences Leopoldina [LPDS 2021-02]
- French National Research Agency [ANR-20-CE47-0005]
- U.S.-ARO Contract [W911NF1310172]
- NSF [DMR-2037158]
- Simons Foundation
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The statistics of energy eigenvalues are important for understanding many-body quantum chaos, and partial spectral form factors can provide insights into subsystems of many-body systems. We propose a protocol that uses randomized measurements to measure the spectral form factor and partial spectral form factors in quantum many-body spin models.
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.
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