The Fermion-ladder Models: Extentions of the Hubbard Model with η-pairing

We propose the two-leg fermion-ladder models for SU(2|2) and SU(4) cases. The former is exactly the extended Hubbard model proposed by Essler, Korepin and Schoutens. The later is a new model also with η-pairing symmetry which is important for superconductivity. This new extension of the Hubbard model can be solved exactly. PACS: 75.10.Jm, 71.10.Fd, 05.30.Fk. Since the discovery of high-temperature superconductivity, much more attention has been paied to the theoretical mechanism for such phenomena. Most proposals concern about the Hubbard model and the t − J model [1]. C.N.Yang [2] mentioned the importance of η-pairing mechanism and the property of off-diagonal long-range order (ODLRO) for the eigenfunctions in superconductivity. Essler, Korepin and Schoutens [3] propsed an extended Hubbard model with η-pairing symmetry. They showed that the states of this extended Hubbard model exhibite ODLRO and is thus superconducting. In [4], the authors introduced the interlayer tunneling mechanism to explain the superconductivity. And the gap equation can be derived by considering two close CuO layers described by the BCS reduced Hamiltonian and coupled by the momentun conserving Josephson pair tunneling term. Recently, both in experiment and theory, there also has been growing interest in the spin ladders for their relevance to some quasi-one-dimensional materials, which under hole-doping may show superconductivity[5]. And many spin-ladder models and fermion-ladder models including t − J ladders and Hubbard ladders are proposed [6]. In this letter, motivated by the the construction of spin-ladder models, we study the coupled fermion models. We construct the most simple fermion-ladder models for SU(2|2) and SU(4) cases. The first one gives the extended Hubbard model which has already been studied[3], the second is a new extended Hubbard model which also has the symmetry of η-pairing and its eigenfunctions possess ODLRO. Generally, we will concentrate on the integrable models which can be solved exactly. We first start from the integrable one-dimensional fermion chain with SU(1|1) symmetry. Electrons on a lattice are described by canonical Fermi operators satisfying {ai , aj} = δij . The Fock vacuum state |0 > satisfies ∗Permanent address: Institute of Modern Physics, Northwest University, Xi’an 710069, P.R.China