arXiv:1206.2630 · Journal of Statistical Mechanics Theory and Experiment

Form factor approach to dynamical correlation functions in critical models

N Kitanine, Karol Kajetan Kozlowski, Jean Michel Maillet, N. A. Slavnov, V. Terras

Published Sep 6, 2012• 165 citations

Abstract

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schrödinger model. We derive the long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle–hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on a microscopic analysis of the model, without invoking, at any stage, any correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, possibly with minor modifications, to a wide class of (not necessarily integrable) gapless one-dimensional Hamiltonians.

DOI: 10.1088/1742-5468/2012/09/p09001

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