Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: complete spectrum and matrix elements of some quasi-local operators

作者：Niccoli G^*

来源：Journal of Statistical Mechanics: Theory and Experiment , 2012, P10025.

DOI：10.1088/1742-5468/2012/10/P10025

• integrable spin chains (vertex models)
• quantum integrability (Bethe ansatz)

The integrable quantum models, associated with the transfer matrices of the 6-vertex reflection algebra for spin-1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide the complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. Moreover, we use these integrable quantum models as further key examples for which to develop a method in the SOV framework to compute matrix elements of local operators. This method is based on the resolution of the quantum inverse problem (i.e. the reconstruction of local operators in terms of the quantum separate variables) plus the computation of the action of separate covectors on separate vectors. In particular, for these integrable quantum models, which in the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with non-diagonal boundary conditions, we have obtained the SOV-reconstruction for a class of quasi-local operators and determinant formulae for the covector-vector actions. As a consequence of these findings we provide one determinant formula for the matrix elements of this class of reconstructed quasi-local operator on transfer matrix eigenstates.

• 出版日期2012-10