Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation

We consider the one-dimensional XXX spin 1/2 Heisenberg 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 n ≤ 6 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 n. on leave of absence from the Institute for High Energy Physics, Protvino, 142284, Russia Membre du CNRS