H.E.Boos, V.E.Korepin, Y.Nishiyama, M.Shiroishi
Quantum Correlations and Number Theory
(215K, Postscript)

ABSTRACT.  We study spin-1/2 Heisenberg XXX antiferromagnet. The spectrum of the 
Hamiltonian was found by Hans Bethe in 1931. We study the probability 
of formation of ferromagnetic string in the antiferromagnetic ground 
state, which we call emptiness formation probability P(n). This is the 
most fundamental correlation function. We prove that for the short 
strings it can be expressed in terms of the Riemann zeta function with 
odd arguments, logarithm ln 2 and rational coefficients. This adds yet 
another link between statistical mechanics and number theory. We have 
obtained an analytical formula for P(5) for the first time. We have also 
calculated P(n) numerically by the Density Matrix Renormalization 
Group. The results agree quite well with the analytical ones. 
Furthermore we study asymptotic behavior of P(n) at finite temperature 
by Quantum Monte-Carlo simulation. It also agrees with our previous 
analytical results.