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Journal of Mathematical Physics

Symplectic symmetry of Hubbard model and η pairing

Chunyan Sun, B. F. Li, Z. S. Li

Published Mar 1, 1995• 2 citations
Publisher

Abstract

By means of symplectic group Sp(2M), the symplectic symmetry of the Hubbard model and the η pairing are investigated to approach the eigenstates which have the largest spin multiplicities. The behavior of the off-diagonal long-range order of these eigenstates is examined by the criterion proposed by Yang and the energy diagram of the corresponding eigenvalues is elucidated by the η pairing mechanism. A basis set which is expressible in terms of η and ηa pairings is proposed.

DOI
10.1063/1.531363

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By means of symplectic group Sp(2M), the symplectic symmetry of the Hubbard model and the η pairing are investigated to approach the eigenstates which have the largest spin multiplicities. The behavior of the off-diagonal long-range order of these eigenstates is examined by the criterion proposed by Yang and the energy diagram of the corresponding eigenvalues is elucidated by the η pairing mechanism. A basis set which is expressible in terms of η and ηa pairings is proposed.
Yang's η pairing operator is generalized to explore off-diagonal long-range order in the Hubbard bilayer with an arbitrary chemical potential. With this operator and a constraint condition on annihilation and creation operators, we construct explicitly eigenstates which possess simultaneously three kinds of off-diagonal long-range order, i.e., the intralayer one and the interlayer one for on-site pairing, and that for interlayer nearest-neighbor pairing. As in the simple Hubbard model there is also an SO(4) symmetry, with the generators properly defined. A sufficient condition leads to at least one of the above three kinds of off-diagonal long-range order. A constraint relation among different kinds of off-diagonal long-range order is also given. There exists a triplet of collective modes if the U(1) symmetry of a subgroup is spontaneously broken.
We consider NNN-particle generalizations of $\ensuremath{\eta}$-pairing states in a chain of NNN-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU(N)\mathrm{SU}(N)SU(N) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd NNN. When NNN is even, these states exhibit off-diagonal long-range order in NNN-particle reduced density matrix. On the other hand, when NNN is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.