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

TL;DR

This paper uses Sklyanin's quantum separation of variables to fully characterize the spectrum and form factors of antiperiodic spin-1/2 XXZ chains, providing explicit formulas and reconstructions.

Contribution

It offers a complete spectrum characterization, operator reconstruction, and determinant formulas for scalar products and form factors in antiperiodic XXZ chains using SOV.

Findings

Complete spectrum and eigenstates characterized

Determinant formulas for scalar products derived

Explicit form factors for local spin operators obtained

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.