Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model

Abstract

Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schrödinger model. This representation allows one to \textit{read-off} straightforwardly the long-time/large-distance asymptotic behavior of this correlator. This method of analysis reduces the complexity of the computation of the asymptotic behavior 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 by using the CFT/Luttinger liquid based predictions.

75 pages, 6 figures, V2, some comments added

References in corpus (2)

• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas

Cited by in corpus (3)

• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint