H.E. Boos , V.E. Korepin, F.A. Smirnov
Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov
Equation
(66K, LTEX)
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.