Correlation functions of integrable $O(n)$ spin chains

TL;DR

This paper analyzes the correlation functions of integrable $O(n)$ spin chains, providing explicit solutions for two-site density matrices for various $n$ at zero temperature, advancing understanding of their quantum properties.

Contribution

It offers explicit solutions to the functional equations for the density matrix of $O(n)$ spin chains, a novel step in understanding their correlation functions.

Findings

Explicit two-site density matrix elements for $O(n)$ spin chains.

Solutions evaluated for $n=3,4, ext{...},8$ at zero temperature.

Enhanced understanding of correlation functions in integrable models.

Abstract

We study the correlation functions of the integrable $O(n)$ spin chain in the thermodynamic limit. We addressed the problem of solving functional equations of the quantum Knizhnik Zamolodchikov type for density matrix related to the $O(n)$ spin chain. We give the explicit solution for two-sites density matrix elements for the $O(n)$ which are then evaluated for the $n=3,4,\dots,8$ cases at zero temperature.