New Supersymmetric and Exactly Solvable Model of Correlated Electrons.

A new lattice model is presented for correlated electrons on the unrestricted 4-dimensional electronic Hilbert space ⊗n=1C (where L is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin and Schoutens. The supersymmetry algebra of the new model is superalgebra gl(2|1). The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter U , and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreps of gl(2|1). On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz. PACS numbers: 71.20.Ad, 75.10.Jm ∗Address after March 16, 1995: Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto, Japan. The Hubbard model and the t-J model, both models of correlated electrons on a lattice, and exactly solvable in one dimension, have been extensively studied due to their promising role in theoretical condensed-matter physics and possibly in high-Tc superconductivity. The t-J model is a lattice model on the restricted 3-dimensional electronic Hilbert space ⊗n=1C (throughout the paper, L is the lattice length), where the occurrence of two electrons on the same lattice site is forbidden. With the special choice of parameters: t = 1 and J = 2, the t-J model becomes supersymmetric with the symmetry algebra being the superalgebra gl(2|1) [1, 2]. In [3, 4, 5], Essler, Korepin and Schoutens (EKS) proposed a model, the so-called extended Hubbard model, of correlated electrons on the unrestricted 4-dimensional electronic Hilbert space⊗n=1C . This EKS model, which allows doubly occupied sites and combines and extends some of the interesting features of the Hubbard model and the t-J model, is exactly solvable in one dimension and has gl(2|2) supersymmetry. In this Letter, we propose another direction of generalization of the Hubbard model. Specifically, we propose a new model on the same unrestricted 4-dimensional electronic Hilbert space ⊗n=1C, but with quite different interaction terms from the ones in the EKS model. Our model has gl(2|1) supersymmetry and contains one symmetry-preserving free real parameter which is exactly the Hubbard interaction parameter U ; this real parameter U has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreps of gl(2|1). The model can naturally be regarded as a modified Hubbard model with additional nearest-neighbor interactions and is again exactly solvable on a one dimensional lattice. The exact solvability of our model in one dimension comes from the fact that as an abstract dynamical model it is derived from a gl(2|1)-invariant rational R-matrix which satisfies the (graded) quantum Yang-Baxter equation (QYBE). It seems that only a gl(2|1)-symmetric lattice model on the unrestricted 4-dimensional electronic Hilbert space could be a natural candidate for the lattice analogue of N=2 superconformal field theory, of which the gl(2|1) = osp(2|2) algebra defines the underlying symmetry, and which is a critically fixed point of the N=2 supersymmetric Landau-Ginzburg model [6]. This gives another motivation for our model. Let us begin by introducing some notation as in [3]. Electrons on a lattice are described