Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors

Abstract

In this paper we consider the spin-1/2 highest weight representations for the 6-vertex Yang–Baxter algebra on a finite lattice and analyze the integrable quantum models associated to the antiperiodic transfer matrix. For these models, which in the homogeneous limit reproduces the XXZ spin-1/2 quantum chains with antiperiodic boundary conditions, we obtain in the framework of Sklyaninʼs quantum separation of variables (SOV) the following results: I) The complete characterization of the transfer matrix spectrum (eigenvalues/eigenstates) and the proof of its simplicity. II) The reconstruction of all local operators in terms of Sklyaninʼs quantum separate variables. III) One determinant formula for the scalar products of separates states, the elements of the matrix in the scalar product are sums over the SOV spectrum of the product of the coefficients of the states. IV) The form factors of the local spin operators on the transfer matrix eigenstates by one determinant formulae given by simple modifications of the scalar product formulae.