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arXiv:hep-th/0602080 · Annales Henri Poincaré

The Elliptic Scattering Theory of the 1/2-XYZ and Higher Order Deformed Virasoro Algebras

Davide Fioravanti A, Marco Rossi

Published Nov 24, 2006• 7 citations
arXivHTMLPDF
DOI
10.1007/s00023-006-0287-3

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We consider an algebraic structure of the XXZXXZXXZ model in the gapless regime. We argue that a certain degeneration limit of the elliptic algebra Aq,p(sl2^)A_{q,p}(\widehat{sl_2})Aq,p​(sl2​​) is a relevant object. We give a free boson realization of this limiting algebra and derive an integral formula for the correlation function. The result agrees with the one obtained by solving a system of difference equations. We also discuss the relation of our algebra to the deformed Virasoro algebra and Lukyanov's bosonization of the sine-Gordon theory.
A lattice Virasoro algebra is constructed for the Baxter eight-vertex model. The operator L0{\mathrm{L}}_{0}L0​ is obtained from the logarithm of the corner transfer matrix and is given by the first moment of the XYZ spin-chain Hamiltonian. The algebra is valid even when the Hamiltonian includes a mass term, in which case it represents lattice coordinate transformations which distinguish between even and odd sublattices. We apply the quantum inverse scattering method to demonstrate that the Virasoro algebra follows from the Yang-Baxter relations.