Finite-size scaling of out-of-time-ordered correlators at late times
Abstract
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to 0 with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to 0 and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.
Additional Information
© 2019 American Physical Society. Received 2 January 2018; revised manuscript received 11 May 2018; published 1 July 2019. We thank Xie Chen, Yingfei Gu, Nick Hunter-Jones, Alexei Y. Kitaev, and Douglas Stanford for helpful discussions. We are especially grateful to X. C., who wrote a substantial portion of this Letter. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1733907). Additional funding support was provided by NSF Grant No. DMR-1654340 (Y. H. and Y.-L. Z.).Attached Files
Published - PhysRevLett.123.010601.pdf
Submitted - 1705.07597.pdf
Supplemental Material - SM.pdf
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Additional details
- Eprint ID
- 79397
- Resolver ID
- CaltechAUTHORS:20170726-091047115
- Institute for Quantum Information and Matter (IQIM)
- PHY-1733907
- NSF
- DMR-1654340
- NSF
- Created
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2017-07-26Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter