Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrodinger model

Abstract

We find that the quantum monodromy matrix associated with a derivative nonlinear Schrodinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse scattering method which is directly applicable to field theoretical models, we derive all possible commutation relations among the operator valued elements of such monodromy matrix. Thus, we obtain the commutation relation between creation and annihilation operators of quasi-particles associated with DNLS model and find out the $S$-matrix for two-body scattering. We also observe that, for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles which can form a soliton state for the quantum DNLS model.

17 pages, Latex, minor typos corrected, to be published in Nucl. Phys. B

References in corpus (4)

• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Complete integrability of derivative nonlinear Schrödinger-type equations
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy

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• Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
• New series of integrable vertex models through a unifying approach
• Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model
• Clusters of bound particles in the derivative delta-function Bose gas
• Clusters of bound particles in a quantum integrable many-body system and number theory
• Exact solvability and quantum integrability of a derivative nonlinear Schrodinger model
• Fermionic dual of one-dimensional bosonic particles with derivative delta function potential