Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrodinger model

TL;DR

This paper applies algebraic Bethe ansatz to a quantum derivative nonlinear Schrödinger model, revealing its symmetry properties, deriving operator relations, and analyzing soliton formation constraints.

Contribution

It introduces a quantum inverse scattering approach for the DNLS model, deriving all operator commutation relations and the two-body S-matrix.

Findings

Quantum monodromy matrix exhibits U(2) or U(1,1) symmetry.

Derived the S-matrix for two-particle scattering.

Found an upper bound on quasi-particle number for soliton states.

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.