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

Abstract

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.

arXiv comment36 pages, 12 figures, second resubmission to SciPost (changes in Introduction and Conclusion, better perturbation and corresponding simulations)

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• Emergent phenomena in Nature: a paradox with Theory?
• Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior
• The classical limit of Schrödinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon
• The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems