Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking

Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schroedinger operators with double well potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985)...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: C J F van de Ven, Groenenboom, G C, Reuvers, R, Landsman, N P
Format: Article
Language:English
Subjects:
Broken symmetry
Operators (mathematics)
Online Access:Get full text
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Summary:Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schroedinger operators with double well potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985) and for quantum spin systems in the thermodynamic limit (Anderson, 1952; Tasaki, 2019). We relate these to each other in the context of the Curie-Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schroedinger operator with double well potential.
ISSN:2331-8422
DOI:10.48550/arxiv.1811.12109