Non-existence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!
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Published:2023-10-27
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Volume:
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ISSN:0129-055X
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Container-title:Reviews in Mathematical Physics
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language:en
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Short-container-title:Rev. Math. Phys.
Affiliation:
1. Institute of Science and Engineering, Faculty of Mechanical Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
Abstract
The Kubo–Martin–Schwinger (KMS) condition is a well-founded general definition of equilibrium states on quantum systems. The time invariance property of equilibrium states is one of its basic consequences. From the time invariance of any equilibrium state it follows that the spontaneous breakdown of time-translation symmetry is impossible. Moreover, triviality of the temporal long-range order is derived from the KMS condition. Therefore, the manifestation of genuine quantum time crystals is impossible as long as the standard notion of spontaneous symmetry breakdown is considered.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Mathematical Physics,Statistical and Nonlinear Physics