Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-12-22
J. Phys. A: Math. Theor. 44 (2011) 335005
Physics
Condensed Matter
Statistical Mechanics
20 pages; details of the derivation are added, comments on different regimes are given
Scientific paper
10.1088/1751-8113/44/33/335005
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.
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