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arXiv:1312.5089 · Journal of Statistical Mechanics Theory and Experiment

Large-distance asymptotic behaviour of multi-point correlation functions in massless quantum models

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

Published May 16, 2014• 44 citations
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Abstract

We provide a microscopic model setting that allows us to readily access the large-distance asymptotic behaviour of multi-point correlation functions in massless, one-dimensional, quantum models. The method of analysis we propose is based on the form factor expansion of the correlation functions and does not build on any field theory reasoning. It constitutes an extension of the restricted sum techniques leading to the large-distance asymptotic behaviour of two-point correlation functions obtained previously.

DOI
10.1088/1742-5468/2014/05/p05011

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We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Luttinger liquid approach, the conformal field theory predictions and our previous analysis of the correlation functions from their multiple-integral representations. We argue that our scheme applies to a general class of non-integrable quantum critical models as well.
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Abstract We derive an explicit expression for the leading term in the long-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This expression is valid for all nonzero finite temperatures and for all magnetic fields below the saturation threshold. It is obtained here by means of a straightforward term-by-term analysis of a thermal form factor series, derived in previous work, and demonstrates the usefulness of the latter.