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

Abstract

Izergin-Korepin's lattice discretization of the non-linear Schrödinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic parameters.

23 pages

References in corpus (4)

• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Integrability of a family of quantum field theories related to sigma models
• Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model

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• On form-factor expansions for the XXZ chain in the massive regime
• Microscopic approach to a class of 1D quantum critical models
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Relaxation of phonons in the Lieb-Liniger gas by dynamical refermionization
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• The relevant excitations for the one-body function in the Lieb-Liniger model