Quantum spin chains and Riemann zeta function with odd arguments
H. Boos, V. E. Korepin · Journal of Physics A Mathematical and General · 2001
The Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.