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Physical review. B, Condensed matter

η mechanism and Berry’s phase in the Hubbard model with a long-range interaction

Yue-lin Shen, Mo‐Lin Ge

Published Oct 15, 1995• 0 citations
Publisher

Abstract

We find eigenstates for a 1/r Hubbard model in terms of the \ensuremath{\eta} pairing mechanism and prove that the model exhibits SO(4) symmetry in its modified form. It turns out that in the presence of a constant magnetic field the \ensuremath{\eta} states share Berry's phase in the adiabatic limit.
DOI
10.1103/physrevb.52.11773

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The existence of $\ensuremath{\eta}$-pairing eigenstates in the fermionic Hubbard model is fundamentally rooted in the $\ensuremath{\eta}$-pairing symmetry, which may hold for systems with nonuniform Hubbard interaction UUU. In this work, we present a generalized Hubbard model containing a variety of pseudospin terms that break the SO4{\mathrm{SO}}_{4}SO4​ symmetry but retain the $\ensuremath{\eta}$-pairing symmetry. This allows us to construct a variety of correlated systems possessing $\ensuremath{\eta}$-pairing eigenstates. We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-$\ensuremath{\eta}$-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a method for the control of an $\ensuremath{\eta}$-pairing wave packet with the aid of a time-dependent Hamiltonian.
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.
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