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Register a new userHidden 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.
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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 Zamolodchikovs integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.
In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the disorder operator itself is considered as primary field. In our previous paper, we have introduced the annhilation operators which mutually anti-commute and kill the primary field. Here we construct the creation counterpart and prove the canonical anti-commutation relations with the annihilation operators. We show that the ground state averages of quasi-local operators created by the creation operators from the primary field are given by determinants.
We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $rho(z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $omega(z,xi)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
We present an expression for the generating function of correlation functions of the sine-Gordon integrable field theory on a cylinder, with compact space. This is derived from the Destri-De Vega integrable lattice regularization of the theory, formulated as an inhomogeneous Heisenberg XXZ spin chain, and from more recent advances in the computations of spin form factors in the thermodynamic limit.
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