2007/01/31 by Jens Damerau, Frank Göhmann, Nils P. Hasenclever +2 · 70 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cauchy distribution #Chain (unit) #Combinatorics #Conjecture #Density matrix #Double exponential function #Exponent #Exponential formula #Exponential function #Factorization #Ground state #Isotropy #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1088/1751-8113/40/17/002
published in Journal of Physics A Mathematical and Theoretical 40(17), 4439-4453 (Institute of Physics) · 19 pages, Latex, 3 figures; v2 minor corrections, a reference updated, v3 typos in the text and in eq. (54) corrected
openalex publication_date 2007/04/11 · arxiv created 2011/09/01 · arxiv updated 2011/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive a multiple integral representing the ground-state density matrix of a segment of length m of the XXZ spin chain on L lattice sites, which depends on L only parametrically. This allows us to treat chains of arbitrary finite length. Specializing to the isotropic limit of the XXX chain we show for small m that the multiple integrals factorize. We conjecture that this property holds for arbitrary m and suggest an exponential formula for the density matrix which involves only a double Cauchy type integral in the exponent. We demonstrate the efficiency of our formula by computing the next-to-nearest neighbour zz -correlation function for chain lengths ranging from two to macroscopic numbers.