Integrable model of interacting XX and Fateev-Zamolodchikov chains

We consider the exact solution of a model of correlated particles, which is presented as a system of interacting XX and Fateev-Zamolodchikov chains. This model can also be considered as a generalization of the multiband anisotropic t − J model in the case we restrict the site occupations to at most two electrons. The exact solution is obtained for the eigenvalues and eigenvectors using the Bethe-ansatz method. PACS numbers: 75.10.Lp, 74.20-z, 71.28+d Typeset using REVTEX 1 It is well known that in the limit of a strong Coulomb repulsion U the traditional Hubbard model reduces to the so-called t − J model [1]. The strong on-site correlations limit the site occupations to at most one electron. States with double occupation on a given site are energetically unfavorable and can be projected out from the Hilbert space. In one dimension this model is integrable at the supersymmetrical point [2 5]. The exact solution can be obtained also for the extension of the supersymmetric spin-1/2 t− J model (i.e. N = 2) to the case of arbitrary number N of bands, having a SU(N) symmetry [6,7], as well as for their anisotropic version [8,9]. In some sense all these models can be considered as a system of interacting XX and XXZ chains with size occupations limited to at most one electron per site [2]. In this paper we consider a generalization of the multiband t − J model for the case where the on-site correlations are enough strong to limit the site occupations to at most two electrons. The exact integrable model we will present can be considered as a system of interacting XX and spin-1 Fateev-Zamolodchikov chains [10,11]. In order to present our model let us consider initially a general model with N distinct type of bands (α = 1, . . . , N) split into two disjoint groups א1 and א2. Taking into account the constraint of maximum double occupancy in a given site we can have at most one electron in bands α ∈ א1 and at most two electrons in bands α ∈ א2. The states of a given site are denoted by |α, β > (α ≤ β, α, β = 0, 1, . . . , N), where in the case α, β = 1, 2, . . .N these are the bands where the electrons are located while α = 0 or β = 0 denotes the absence of electrons. As a conequence of this notation the state |α, α > is forbidden if α ∈ א1 and it is allowed if α ∈ א2 or α = 0. The most general Hamiltonian with nearestneighbours interactions, in a lattice with L sites and periodic boundary condition, that conserves separately the electrons in each band can be written as H = − L