Emptiness formation probability and quantum Knizhnik–Zamolodchikov equation

Abstract

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.