1206.0646 (G. Niccoli)

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

G. Niccoli

The integrable quantum models associated to the transfer matrices of spin 1/2 highest weight representations for the 6-vertex reflection algebra are studied in the framework of Sklyanin's quantum separation of variables (SOV). 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 provide: I) The complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. II) The reconstruction of a class of quasi-local operators in terms of the Sklyanin's quantum separate variables. III) The scalar products of separates states by one determinant formula where the elements of the matrix are sums over the SOV spectrum of the product of the coefficients of the states. IV) One determinant formula for the form factors on transfer matrix eigenstates of the class of reconstructed quasi-local operators; form factors which are characterized by simple modifications of the elements of the matrices entering in the scalar products.

View original: http://arxiv.org/abs/1206.0646