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Annales Henri Poincaré

, Volume 16, Issue 2, pp 437–534 | Cite as

Large-Distance and Long-Time Asymptotic Behavior of the Reduced Density Matrix in the Non-Linear Schrödinger Model

  • Karol Kajetan KozlowskiEmail author
Article

Abstract

Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the time- and distance-dependent reduced density matrix at zero temperature in the non-linear Schrödinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behaviour of this correlator. This method of analysis reduces the complexity of the computation of the asymptotic behaviour of correlation functions in the so-called interacting integrable models, to the one appearing in free-fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained using the CFT/Luttinger liquid-based predictions.

Keywords

Form Factor Holomorphic Function Thermodynamic Limit Reduce Density Matrix Translation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Basel 2014

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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