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arXiv · 1206.2630

Form factor approach to dynamical correlation functions in critical models

N. Kitanine·K. K. Kozlowski·J. M. Maillet·N. A. Slavnov·V. Terras
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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 Schr\"odinger model. We derive 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 the microscopic analysis of the model, without invoking, at any stage, some 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, with possibly minor modifications, to a wide class of (not necessarily integrable) gapless one dimensional Hamiltonians.

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N. Kitanine, K. K. Kozlowski, J. M. Maillet, N. A. Slavnov, V. Terras. 2012-06-12. Form factor approach to dynamical correlation functions in critical models. https://doi.org/10.1088/1742-5468%2F2012%2F09%2Fp09001

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