Exact evaluation of density matrix elements for the Heisenberg chain

TL;DR

This paper analytically computes all density matrix elements and eigenvalues for a six-site segment of the spin-1/2 Heisenberg chain, enabling exact evaluation of correlation functions and von Neumann entropy.

Contribution

It provides the first exact algebraic calculation of the full density matrix and its eigenvalues for a six-site Heisenberg chain segment, including various correlation functions.

Findings

Exact density matrix elements for six sites obtained

Eigenvalues of the density matrix calculated

Von Neumann entropy explicitly determined

Abstract

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a result the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.