Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

TL;DR

This paper characterizes the spectrum and form factors of antiperiodic higher spin XXX chains using quantum separation of variables, extending previous methods to more general representations and providing explicit determinant formulas.

Contribution

It generalizes the quantum separation of variables approach to antiperiodic higher spin chains, deriving the complete spectrum, simplicity, and form factors with explicit formulas.

Findings

Complete spectrum characterization of the transfer matrix.

Proof of simplicity of the spectrum.

Determinant formulas for form factors.

Abstract

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the spin-1/2 highest weight representations, and in [3], for the spin 1/2 representations of the reflection algebra. Here, we derive the complete characterization of the transfer matrix spectrum and we prove its simplicity in the framework of Sklyanin's quantum separation of variables (SOV). Then, the characterization of local operators by Sklyanin's quantum separate variables and the expression of the scalar products of separates states by determinant formulae allow to compute the form factors of the local spin operators by one determinant formulae similar to the scalar product ones. Finally, let us comment that these results represent the SOV analogous in the antiperiodic higher spin XXX quantum chains of the results obtained for the periodic chains in [4] in the framework of the algebraic Bethe ansatz.