Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain

TL;DR

This paper analyzes the correlations in the XXX Heisenberg spin 1/2 antiferromagnet by evaluating the probability of ferromagnetic string formation, revealing a connection to the Riemann zeta function for short strings.

Contribution

It provides a novel analytical expression for the probability of ferromagnetic string formation in the ground state, linking it to the Riemann zeta function for the first time.

Findings

Probability expressed via Riemann zeta function for short strings

Analytical results in the thermodynamic limit

Insights into spin correlation functions

Abstract

We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.