Determinant representation for correlation functions of spin-1/2 XXX and XXZ Heisenberg magnets

1994/06/30 by F. H. L. Essler, Fabian H. L. Eßler, Holger Frahm +3 · 82 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Cold Atom Physics and Bose-Einstein Condensates #Ferromagnetism #Fredholm determinant #Heisenberg model #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum electrodynamics #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #cond-mat #hep-th

paper · pdf · doi:10.1007/bf02099470

published in Communications in Mathematical Physics 174(1), 191-214 (Springer Science+Business Media) · 23 pages, TeX, BONN-TH-94-14, revised version: typos corrected

arxiv created 1994/09/22 · openalex publication_date 1995/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider correlation functions of the spin-\half XXX and XXZ Heisenberg chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in terms of determinants of Fredholm integral operators.

Citations

• The Dynamical Correlation Function of the XXZ Model
• Difference equations for the correlation functions of the eight-vertex model
• Quantum inverse problem method. I
• Calculation of norms of Bethe wave functions
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS
• Two soluble models of an antiferromagnetic chain
• Correlation function of the spin- XXX antiferromagnet