Abstract Some electromagnetic properties of the η‐pairing eigenstate of the Hubbard model are investigated. The persistent current density Js in the eigenstate is discussed, and the distribution of magnetic field in the studied periodic lattice is analyzed. It is shown that the behaviour of the electromagnetic response is peculiar.
Abstract The symmetry and the eigenstates of the 3D Hubbard model in the presence of an external electromagnetic field on a periodic simple cubic lattice are investigated within the pseudospin and spin framework. It is shown that the magnetic flux through the periodic lattice is quantized in units of hc/2e, and in this situation the Hubbard system possesses SO4 symmetry which is proved to be spontaneous breaking in the eigenstates obtained explicitly of the model. The information of ODLRO in those eigenstates is also discussed. The absolute ground state of the Hubbard model is yet obtained, and found that the state may not show superconducting transition.
The Hubbard model in bipartite lattice has been rigorously proved to have $\ensuremath{\eta}$-paired states as eigenstates by C. N. Yang [Phys. Rev. Lett. 63, 2144 (1989)]. In this paper, this result is first generalized to a triangular lattice and then even to an arbitrary lattice structure. We also consider its generalization to higher-spin Hubbard models. The conditions under which these models have $\ensuremath{\eta}$-paired states as eigenstates were obtained.
Abstract We investigate Hubbard models with bond–charge interactions on general graphs. For a Hamiltonian H of such a model, we provide the condition on its parameters under which the η -pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the η -pairing state ( η † ) N ∣ 0 〉 to be an eigenstate of H is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian H m without bond–charge interactions. When the condition for ( η † ) N ∣ 0 〉 to be an eigenstate of the Hubbard-type Hamiltonian H m is satisfied, we demonstrate that there are additional states, distinct from ( η † ) N ∣ 0 〉 , which are also exact eigenstates of H m . Our results enhance the understanding of Hubbard models on general graphs, both with and without bond–charge interactions.