Berlin 2012 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 45: Correlated Electrons: Poster Session

TT 45.45: Poster

Donnerstag, 29. März 2012, 15:00–19:00, Poster B

Correlation functions of the spin-1/2 Heisenberg chain at finite temperature via functional equations — •Britta Aufgebauer and Andreas Klümper — Bergische Universität Wuppertal

We present results on static finite temperature correlation functions of the Heisenberg chain on arbitrary successive sites in the thermodynamic limit. The density matrix, encoding all information about the correlation functions on a fixed number of successive sites, is obtained in a suitable limit of the six-vertex model density matrix on a rectangular lattice of unbounded width and finite height with toroidal boundary conditions. We consider an inhomogeneous density matrix. The inhomogeneities enable the derivation of a functional equation of difference type, valid for a finite set of parameter values. This equation in conjunction with the asymptotic behaviour determines the inhomogeneous density operator uniquely.

The functional equation is a discrete version of the so-called reduced quantum Knizhnik-Zamolodchikov equation fulfilled by the density operator at zero temperature. Despite the fundamentally different analytical properties of the correlation functions, it follows that the algebraic structure survives the introduction of a non-zero temperature. In particular the physical input for the calculation of correlation functions on arbitrary successive sites is a finite number of one- and two-point functions.