Exact evaluation of density matrix elements for the Heisenberg chain

2006/11/06 by Jun Sato, Masahiro Shiroishi, Minoru Takahashi · 27 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Chain (unit) #Density matrix #Eigenvalues and eigenvectors #Entropy (arrow of time) #Lattice (music) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Von Neumann entropy #cond-mat.stat-mech #hep-th #nlin.SI #quant-ph

paper · pdf · doi:10.1088/1742-5468/2006/12/p12017

published in Journal of Statistical Mechanics Theory and Experiment 2006(12), P12017 (Institute of Physics) · 33 pages, 4 eps figures, 3 authors

arxiv created 2006/11/06 · openalex publication_date 2006/12/21 · arxiv updated 2011/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/09

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 analyse the eigenvalue distribution. As a result, the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.

Citations

• Current algebra and Wess-Zumino model in two dimensions
• Density Matrix of a Finite Sub-chain of the Heisenberg Anti-ferromagnet
• Third-neighbour and other four-point correlation functions of spin-1/2XXZchain
• First principle approach to correlation functions of spin-1/2 Heisenberg chain: fourth-neighbor correlators
• Two soluble models of an antiferromagnetic chain
• Next-nearest-neighbour correlation functions of the spin-1/2XXZchain at the critical region
• Correlation function of the spin- XXX antiferromagnet