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SO(4) symmetry and off-diagonal long-range order in the Hubbard bilayer

Yu Shi
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Abstract

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 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.

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Yu Shi. 1997-03-02. SO(4) symmetry and off-diagonal long-range order in the Hubbard bilayer. https://doi.org/10.1088/0253-6102%2F28%2F1%2F23

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