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.

arXiv comment75 pages, 6 figures, V2, some comments added

References in corpus (10)

• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• Temperature Correlations of Quantum Spins
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Master equation for spin-spin correlation functions of the XXZ chain
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Emptiness formation probability of the XXZ spin-1/2 Heisenberg chain at Delta=1/2
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• The New Identity for the Scattering Matrx of Exactly Solvable Models
• Quantum Projectors and Local Operators in Lattice Integrable Models

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• On Form Factors of the conjugated field in the non-linear Schröodinger model
• 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