Séminaire de Physique ThéoriqueForm factor approach to the asymptotic behavior of correlation functions
Karol Kozlowski (IMB, Dijon)
Thursday 15 March 2012 14:00 - Tours - Salle 1180 (Bât E2)
There exist various approximation methods (CFT, Luttinger liquid, non-linear Luttinger liquid) allowing one to study certain limiting regimes of the behavior of various correlation functions in one dimensional gapless quantum Hamiltonians. In this talk, I will overview the recent developments in respect to setting up yet another approach to characterizing certain properties of the correlatior in one dimensional gapless models. The approach that I will discuss is based on the study of form factor expansions for two-point functions. Under a specific assumption on the structure of the large-volume asymptotic behavior of the form factors and of the spectrum, I will argue that, starting from a gapless model in large but finite volume, it is possible to sum-up the form factor expansion in the largedistance and/or long-time regime. In such a way, one reporduces the CFT and Luttinger-liquid based predictions for the long-distance asymptotics of two-point functions. One is furthermore able to access to the large-distance and long-time asymptotics. Finally, I will also breifly discuss the progress in the computation, starting from the first principles, of the edge exponents characterizing the power-law behavior of the density structure factor and the spectral functions near the edges of the particle or hole excitation tresholds. I will illustrate the talk with examples arising in integrable models such as the XXZ spin-1/2 chain or the non-linear Schrödinger model. In particular, I will show that one reproduces the predictions of the amplitudes and the edge exponents stemming from the use of the non-linear Luttinger liquid theory. These results stem from a joint work with Kitanine, Maillet, Slavnov and Terras.