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Exact solution of the $sp(4)$ integrable spin chain with generic boundaries

169   0   0.0 ( 0 )
 Added by Jun-Peng Cao
 Publication date 2018
  fields Physics
and research's language is English




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The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. For the periodic boundary condition case, we recover the same $T-Q$ relations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneous $T-Q$ relations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to generic $sp(2n)$ (i.e., $C_n$) integrable model.



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By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) 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-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.
An integrable Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and Dzyaloshinski-Moriya interacton is constructed. The integrability of the model is proven. Based on the Bethe Ansatz solutions, the ground state and the elementary excitations are studied. It is shown that the spinon excitation spectrum of the present system possesses a novel triple arched structure. The method provided in this paper is general to construct new integrable models with next-nearest-neighbour couplings.
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