Towards the web of quantum chaos diagnostics

Creators: Bhattacharyya, Arpan; Chemissany, Wissam; Haque, S. Shajidul; Yan, Bin

Abstract

We study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also investigated the relationship between a specific circuit complexity and LE by using the inverted oscillator model and made a conjecture about their relationship. These relationships signal a deeper connection between these three probes of quantum chaos.

Additional Information

© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Funded by SCOAP3. Received 24 August 2021; Accepted 14 January 2022; Published 29 January 2022. The authors would like to thank Aritra Banerjee, Jordan Colter, Jorge Kurchan and Dan Roberts for useful discussions and email exchanges. W.A.C would like to thank the Institute for Quantum Information and Matter (IQIM), Caltech, for the ongoing stimulating environment from which the author has been significantly benefited. A.B is supported by Start-Up Research Grant (SRG/2020/001380) by the Department of Science and Technology Science and Engineering Research Board (India) and Relevant Research Project grant (58/14/12/2021-BRNS) by the Board Of Research In Nuclear Sciences (BRNS), Department of Atomic Energy, India. W.A.C gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). B.Y. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, Condensed Matter Theory Program, and partial support from the Center for Nonlinear Studies. Author Contributions: All authors contributed equally to this paper. Data Availability Statement: This manuscript has no associated data or the data will not be deposited. [Authors' comment: Our calculation doesn't generate any data of any kind. All the results are deposited in the actual draft.]

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