Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrödinger model

Abstract

We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schrödinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics.

47 pages, 2 figures

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• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Correlation lengths of the repulsive one-dimensional Bose gas
• Open XXZ chain and boundary modes at zero temperature
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Correlation functions by Separation of Variables: the XXX spin chain
• Asymptotic behaviour of two-point functions in multi-species models
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint