7,771 research outputs found
Hidden Grassmann structure in the XXZ model V: sine-Gordon model
We study one-point functions of the sine-Gordon model on a cylinder. Our
approach is based on a fermionic description of the space of descendent fields,
developed in our previous works for conformal field theory and the sine-Gordon
model on the plane. In the present paper we make an essential addition by
giving a connection between various primary fields in terms of yet another kind
of fermions. The one-point functions of primary fields and descendants are
expressed in terms of a single function defined via the data from the
thermodynamic Bethe Ansatz equations.Comment: 36 pages. Some corrections are done in latest version, especially in
the subsection 10.
Quantum model of interacting ``strings'' on the square lattice
The model which is the generalization of the one-dimensional XY-spin chain
for the case of the two-dimensional square lattice is considered. The subspace
of the ``string'' states is studied. The solution to the eigenvalue problem is
obtained for the single ``string'' in cases of the ``string'' with fixed ends
and ``string'' of types (1,1) and (1,2) living on the torus. The latter case
has the features of a self-interacting system and looks not to be integrable
while the previous two cases are equivalent to the free-fermion model.Comment: LaTeX, 33 pages, 16 figure
Hidden Grassmann Structure in the XXZ Model IV: CFT limit
The Grassmann structure of the critical XXZ spin chain is studied in the
limit to conformal field theory. A new description of Virasoro Verma modules is
proposed in terms of Zamolodchikov's integrals of motion and two families of
fermionic creation operators. The exact relation to the usual Virasoro
description is found up to level 6.Comment: 44 pages, 1 figure. Version 3: some corrections are don
Connecting lattice and relativistic models via conformal field theory
We consider the quantum group invariant XXZ-model. In infrared limit it
describes Conformal Field Theory with modified energy-momentum tensor. The
correlation functions are related to solutions of level -4 of qKZ equations. We
describe these solutions relating them to level 0 solutions. We further
consider general matrix elements (form factors) containing local operators and
asymptotic states. We explain that the formulae for solutions of qKZ equations
suggest a decomposition of these matrix elements with respect to states of
corresponding Conformal Field Theory .Comment: 22 pages, 1 figur
Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain
We study the generating function of the spin-spin correlation functions in
the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without
magnetic field. We have found its fundamental functional relations from those
for general correlation functions, which originate in the quantum
Knizhink-Zamolodchikov equation. Using these relations, we have calculated the
explicit form of the generating functions up to n=6. Accordingly we could
obtain the spin-spin correlator up to k=5.Comment: 10 page
Exact evaluation of density matrix elements for the Heisenberg chain
We have obtained all the density matrix elements on six lattice sites for the
spin-1/2 Heisenberg chain via the algebraic method based on the quantum
Knizhnik-Zamolodchikov equations. Several interesting correlation functions,
such as chiral correlation functions, dimer-dimer correlation functions, etc...
have been analytically evaluated. Furthermore we have calculated all the
eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a
result the exact von Neumann entropy for the reduced density matrix on six
lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author
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