Form-factors of the finite quantum XY-chain

TL;DR

This paper derives explicit formulas for the matrix elements of spin operators in the finite quantum XY-chain, linking it to related models to facilitate analysis of correlation functions at finite temperature.

Contribution

It provides the first explicit factorized formulas for XY-chain form-factors by relating it to the Ising and Baxter-Bazhanov-Stroganov models, enabling new analytical approaches.

Findings

Derived explicit form-factor formulas for the XY-chain

Linked XY-model form-factors to Ising and axter-Bazhanov-Stroganov models

Re-derived correlation function asymptotics without Toeplitz determinants

Abstract

Explicit factorized formulas for the matrix elements (form-factors) of the spin operators \sigma^x and \sigma^y between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in a transverse field were derived. The derivation is based on the relations between three models: the model of quantum XY-chain, Ising model on 2D lattice and N=2 Baxter-Bazhanov-Stroganov \tau^{(2)}-model. Due to these relations we transfer the formulas for the form-factors of the latter model recently obtained by the use of separation of variables method to the model of quantum XY-chain. Hopefully, the formulas for the form-factors will help in analysis of multipoint dynamic correlation functions at a finite temperature. As an example, we re-derive the asymptotics of two-point correlation function in the disordered phase without the use of the Toeplitz determinants and the Wiener-Hopf factorization method.