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arXiv:1906.07636 · Annales Henri Poincaré

Integral Formulas and Antisymmetrization Relations for the Six-Vertex Model

Luigi Cantini A, Filippo Colomo, A. G. Pronko

Published Oct 9, 2019• 6 citations
arXivHTMLPDF
DOI
10.1007/s00023-019-00856-6

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We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities.