期刊
JOURNAL OF STATISTICAL PHYSICS
卷 174, 期 4, 页码 735-761出版社
SPRINGER
DOI: 10.1007/s10955-018-2193-8
关键词
Long-range order; Spontaneous symmetry breaking; Tower of states; Quantum spin systems
资金
- JSPS [16H02211]
- Grants-in-Aid for Scientific Research [16H02211] Funding Source: KAKEN
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 exhibits 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.
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