Spontaneous Symmetry Breaking in Coupled Bose–Einstein Condensates
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We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal long-range order, we prove that the coupled system exhibits spontaneous symmetry breaking (SSB) in the infinite volume limit, in the sense that the two subsystems maintain a definite relative U(1) phase when the tunneling is turned off. Although SSB of the U(1) phase is never observable in a single system, SSB of the relative U(1) phase is physically meaningful and observable by interference experiments. The present theorem is made possible by the rigorous theory of low-lying states and SSB in quantum antiferromagnets developed over the years.
I wish to thank Akira Shimizu and Masahito Ueda for indispensable discussions and comments which made the present work possible, and Tohru Koma, Akinori Tanaka, and Haruki Watanabe for useful discussions on related topics. I also thank two anonymous referees for useful suggestions. The present work was supported by JSPS Grants-in-Aid for Scientific Research No. 16H02211.
- 5.Leggett, A.J., Sols, F.: On the concept of spontaneous broken gauge symmetry in condensed matter physics. J. Stat. Phys. 21, 353–364 (1991)Google Scholar
- 12.Tasaki, H.: Long-range order, “tower” of states, and symmetry breaking in lattice quantum systems. J. Stat. Phys. 174, 735–761. (The version in the arXiv is more complete than the published version.) arXiv:1807.05847 (2019)
- 13.Tasaki, H.: Physics and Mathematics of Quantum Many-Body Systems. Springer, New York (1987)Google Scholar
- 16.Herring, G., Kevrekidis, P.G., Malomed, B.A., Carretero-Gonzalez, R., Frantzeskakis, D.J.: Symmetry breaking in linearly coupled dynamical lattices. Phys. Rev. E 76, 066606. arXiv:0704.3284 (2007)
- 29.Shimizu, A., Miyadera, T.: Charge superselection rule does not rule out pure states of subsystems to be coherent superpositions of states with different charges, preprint. arXiv:cond-mat/0102429 (2001)
- 30.Shimizu, A., Miyadera, T.: Robustness of wave functions of interacting many Bosons in a leaky box. Phys. Rev. Lett. 85, 688–691 (2000). (Errata: Phys. Rev. Lett. 86, 4422 (2001))Google Scholar
- 32.Tasaki, H.: Statistical Mechanics, (Baifukan, 2008). The English version by H. Tasaki and G. Paquette is in preparation (2008) (in Japanese)Google Scholar