Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elements

We continue our investigation of the Z_N-Baxter-Bazhanov-Stroganov model using the method of separation of variables [nlin/0603028]. In this paper we calculate the norms and matrix elements of a local Z_N-spin operator between eigenvectors of the auxiliary problem. For the norm the multiple sums over the intermediate states are performed explicitly. In the case N=2 we solve the Baxter equation and obtain form-factors of the spin operator of the periodic Ising model on a finite lattice.Comment: 24 page

Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.Comment: 14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007

Spin operator matrix elements in the quantum Ising chain: fermion approach

Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite length. The derivation is based on the approach recently used to derive factorized formula for Z_N-spin operator matrix elements between ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable chiral Potts quantum chain. The obtained factorized formulas for the matrix elements of Ising chain coincide with the corresponding expressions obtained by the Separation of Variables Method.Comment: 19 page

Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite lattice

We continue our investigation of the Baxter-Bazhanov-Stroganov or \tau^{(2)}-model using the method of separation of variables [nlin/0603028,arXiv:0708.4342]. In this paper we derive for the first time the factorized formula for form-factors of the Ising model on a finite lattice conjectured previously by A.Bugrij and O.Lisovyy in [arXiv:0708.3625,arXiv:0708.3643]. We also find the matrix elements of the spin operator for the finite quantum Ising chain in a transverse field.Comment: 25 pages; sections 8 and A.2 are extended, 2 related references are adde

Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions

This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist fields in the massive Majorana fermion quantum field theory. At finite temperature, these are known to satisfy a set of integrable partial differential equations, including the sinh-Gordon equation. We apply the classical inverse scattering method to study them, finding that the ``initial scattering data'' corresponding to the correlation functions are simply related to the one-particle finite-temperature form factors calculated recently by one of the authors. The set of linear integral equations (Gelfand-Levitan-Marchenko equations) associated to the inverse scattering problem then gives, in principle, the two-point functions at all space and time separations, and all temperatures. From them, we evaluate the large-time asymptotic expansion ``near the light cone'', in the region where the difference between the space and time separations is of the order of the correlation length