Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking
Quantum Physics
2020-02-12 v3
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.
Cite
@article{arxiv.1811.12109,
title = {Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking},
author = {C. J. F. van de Ven and G. C. Groenenboom and R. Reuvers and N. P. Landsman},
journal= {arXiv preprint arXiv:1811.12109},
year = {2020}
}
Comments
36 pages, 12 figures, second resubmission to SciPost (changes in Introduction and Conclusion, better perturbation and corresponding simulations)