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 Sklyanin's 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 Sklyanin's 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 a one determinant formula given by simple modifications of the scalar product formula.

29 pages

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Cited by in corpus (7)

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Exact solution of the XXX Gaudin model with the generic open boundaries
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• The scalar product of XXZ spin chain revisited. Application to the ground state at $\Delta =-1/2$
• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3