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Long-range order, "tower" of states, and symmetry breaking in lattice quantum systems. (arXiv:1807.05847v1 [cond-mat.stat-mech])
来源于:arXiv
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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