Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Phase transitions and Critical Phenomena II

DY 28.1: Topical Talk

Thursday, March 25, 2010, 14:00–14:30, H47

Static correlation functions of integrable quantum chains — •Frank Göhmann — Bergische Universität Wuppertal, Germany

Recently the structure of the correlation functions of the Heisenberg-Ising chain has been completely resolved. After an appropriate regularization they all factorize into sums over products of the one-point function and a single special neighbour two-point function. This resembles the situation with free fermions, and, indeed, what is behind is a remarkable free fermionic structure on the space of (quasi-) local operators on the spin chain. It allows us, for instance, to calculate short-range correlators over the full phase diagram directly in the thermodynamic limit. Numerical values of the correlators can be obtained with arbitrary precision by solving simple and well-behaved integral equations. I shall explain the basic notions behind the factorization and I shall illustrate them with examples. I further advocate the hypothesis that factorization is the characteristic feature of possibly all integrable quantum chains.