Thermal form factors of the XXZ chain and the largedistance asymptotics of its temperature dependent correlation functions
Abstract
We derive expressions for the form factors of the quantum transfer matrix of the spin\frac{1}{2} XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finitetemperature correlation functions of the model. We consider form factor expansions of the longitudinal and transversal twopoint functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of groundstate correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the high and lowtemperature limits. We obtain, in particular, the largedistance asymptotics of the longitudinal twopoint functions for small temperatures by summing up the asymptotically most relevant terms in the form factor expansion of a generating function of the longitudinal correlation functions. As expected, the leading term in the expansion of the corresponding twopoint functions is in accordance with conformal field theory predictions. Here it is obtained for the first time by a direct calculation.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 July 2013
 DOI:
 10.1088/17425468/2013/07/P07010
 arXiv:
 arXiv:1305.0118
 Bibcode:
 2013JSMTE..07..010D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 51 pages, one figure, v2: minor revisions and corrections