11 research outputs found
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
Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov -model for N=2
We find a representation of the row-to-row transfer matrix of the
Baxter-Bazhanov-Stroganov -model for N=2 in terms of an integral over
two commuting sets of grassmann variables. Using this representation, we
explicitly calculate transfer matrix eigenvectors and normalize them. It is
also shown how form factors of the model can be expressed in terms of
determinants and inverses of certain Toeplitz matrices.Comment: 23 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
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Factorized finite-size Ising model spin matrix elements from Separation of Variables
Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted
to the cyclic Baxter--Bazhanov--Stroganov or -model, we derive
factorized formulae for general finite-size Ising model spin matrix elements,
proving a recent conjecture by Bugrij and Lisovyy
Spin operator matrix elements in the superintegrable chiral Potts quantum chain
We derive spin operator matrix elements between general eigenstates of the
superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our
starting point is the extended Onsager algebra recently proposed by R.Baxter.
For each pair of spaces (Onsager sectors) of the irreducible representations of
the Onsager algebra, we calculate the spin matrix elements between the
eigenstates of the Hamiltonian of the quantum chain in factorized form, up to
an overall scalar factor. This factor is known for the ground state Onsager
sectors. For the matrix elements between the ground states of these sectors we
perform the thermodynamic limit and obtain the formula for the order
parameters. For the Ising quantum chain in a transverse field (N=2 case) the
factorized form for the matrix elements coincides with the corresponding
expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur
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