Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation

TL;DR

This paper introduces a new method based on the quantum Knizhnik-Zamolodchikov equation to compute the emptiness formation probability in the inhomogeneous XXX spin chain, revealing connections to number theory.

Contribution

A novel technique for calculating EFP in inhomogeneous systems using quantum KZ equations, with explicit results for length six and a conjecture for general length.

Findings

Computed EFP for length six in inhomogeneous case

Confirmed relation between quantum correlations and number theory

Proposed a conjecture for EFP structure at arbitrary length

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 in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of EFP in the inhomogeneous case. It is based on quantum Knizhnik-Zamolodchikov equation. We evalauted EFP for strings of the length six in the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations to number theory. We also make a conjecture about a general structure of EFP for arbitrary lenght of the string \.