Form-factors of the finite quantum XY-chain

Abstract:
Explicit factorized formulas for the matrix elements (form-factors) of the spin operators between the eigenvectors of the Hamiltonian of finite quantum 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 the N = 2 Baxter-Bazhanov-Stroganov (or τ⁽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 multitime correlation functions at a finite temperature. As an example, we re-derive the asymptotics of two-point correlation function found by Barouch and McCoy without the use of the Toeplitz determinants and the Wiener-Hopf factorization method.