Long-range order, 'tower' of states, and symmetry breaking in lattice quantum systems
arXiv, 2018
Online
unknown
Zugriff:
In a quantum many-body system where the Hamiltonian and the order operator do not commute, it often happens that the unique ground state of a finite system exhibits long-range order (LRO) but does not show spontaneous symmetry breaking (SSB). Typical examples include antiferromagnetic quantum spin systems with Neel order, and lattice boson systems which exhibit Bose-Einstein condensation. By extending and improving previous results by Horsch and von der Linden and by Koma and Tasaki, we here develop a fully rigorous and almost complete theory about the relation between LRO and SSB in the ground state of a finite system with continuous symmetry. We show that a ground state with LRO but without SSB is inevitably accompanied by a series of energy eigenstates, known as the "tower" of states, which have extremely low excitation energies. More importantly, we also prove that one gets a physically realistic "ground state" by taking a superposition of these low energy excited states. The present paper is written in a self-contained manner, and does not require any knowledge about the previous works on the subject.
Comment: 29 pages, 2 figures. This version is more complete than the published version
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Long-range order, 'tower' of states, and symmetry breaking in lattice quantum systems
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Autor/in / Beteiligte Person: | Tasaki, Hal |
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Veröffentlichung: | arXiv, 2018 |
Medientyp: | unknown |
DOI: | 10.48550/arxiv.1807.05847 |
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