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arXiv:1705.09478 · Journal of High Energy Physics

On the Bethe states of the one-dimensional supersymmetric t − J model with generic open boundaries

Pei Sun, Fakai Wen, Kun Hao, Junpeng Cao, Guang-Liang Li, Tao Yang, Wen‐Li Yang, Kangjie Shi

Published Jul 1, 2017• 1 citation
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Abstract

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t − J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T − Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe states which have welldefined homogeneous limit. This exact solution provides basis for further analyzing the thermodynamic properties and correlation functions of the model.

DOI
10.1007/jhep07(2017)051

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By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t − J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T − Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe states which have welldefined homogeneous limit. This exact solution provides basis for further analyzing the thermodynamic properties and correlation functions of the model.
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We propose a novel characterization of the exact solution of the one-dimensional supersymmetric t − J model with generic non-diagonal boundary conditions. Instead of using Bethe roots, we parameterize the eigenvalues of transfer matrix in the spin sector with their zero-roots. By constructing the t − W relation, we obtain the explicit forms of the eigenvalues of the system and the homogeneous Bethe ansatz equations. This scheme is universal and can be applied to other quantum integrable systems with or without U ( 1 ) symmetry.
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Abstract We develop a new method to study the ground state energy of the one-dimensional supersymmetric t – J model with open boundary conditions. The eigenvalues of the nested transfer matrix are characterized by the zero roots of corresponding polynomials instead of the T – Q relation and Bethe roots. The distribution of zero roots at the ground state is studied. We find that the zero roots form two-string pairs, finite pure real and pure imaginary boundary strings. Based on the distribution of zero roots, we obtain the ground state energy of the system in the thermodynamic limit.
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T−Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.
In this paper, we study the surface energy of the one-dimensional supersymmetric t-J model with unparallel boundary magnetic fields, which is a typical U(1)-symmetry broken quantum integrable strongly correlated electron system. It is shown that at the ground state, the contribution of inhomogeneous term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies the finite size scaling law L^β where β<0. Based on it, the physical quantities of the system in the thermodynamic limit are calculated. We obtain the patterns of Bethe roots and the analytical expressions of density of states, ground state energy and surface energy. We also find that there exist the stable boundary bound states if the boundary fields satisfy some constraints.