7,771 research outputs found

    Hidden Grassmann structure in the XXZ model V: sine-Gordon model

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    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

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    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

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    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

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    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

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    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

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    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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