Entanglement asymmetry as a probe of symmetry breaking
Abstract
Symmetry and symmetry breaking are two pillars of modern quantum physics. Still, quantifying how much a symmetry is broken is an issue that has received little attention. In extended quantum systems, this problem is intrinsically bound to the subsystem of interest. Hence, in this work, we borrow methods from the theory of entanglement in many-body quantum systems to introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a prototypical illustration, we study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global U(1) symmetry is restored dynamically. We adapt the quasiparticle picture for entanglement evolution to the analytic determination of the entanglement asymmetry. We find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored, a sort of quantum Mpemba effect, a phenomenon that we show to occur in a large variety of systems.
Additional Information
© The Author(s) 2023. 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/. The authors thank Jerome Dubail, Viktor Eisler, Maurizio Fagotti, Israel Klich, Lorenzo Piroli, Eric Vernier, and Lenart Zadnik for useful discussions. All the authors acknowledge support from ERC under Consolidator grant number 771536 (NEMO). SM thanks support from Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics at Caltech. Contributions. F.A., S.M., and P.C. contributed to the numerical and analytic computations, the interpretation of the results, developing of the theory and the writing of the manuscript. Data availability. The data that support the plots within this paper are provided in the Source Data file. Source data are provided with this paper. Code availability. The computer codes used to generate the results that are reported in this paper are available from the authors upon reasonable request. The authors declare no competing interests.Attached Files
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Supplemental Material - 41467_2023_37747_MOESM2_ESM.xlsx
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Additional details
- PMCID
- PMC10090046
- Eprint ID
- 122032
- Resolver ID
- CaltechAUTHORS:20230628-257227000.37
- European Research Council (ERC)
- 771536
- Institute for Quantum Information and Matter (IQIM)
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2023-06-29Created from EPrint's datestamp field
- Updated
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2023-10-20Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics