02-405 H.E. Boos , V.E. Korepin, F.A. Smirnov

Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation (66K, LTEX) Sep 30, 02

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Abstract. We consider the one-dimensional XXX spin 1/2 antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string $P(n)$ in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik- Zamolodchikov equation [qKZ]. We calculate EFP for a string of lenght six for inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbitrary length of the string.

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