Exact solvability and quantum integrability of a derivative nonlinear Schrodinger model

TL;DR

This paper applies a variant of the quantum inverse scattering method to derive exact solutions and conserved quantities for a quantum derivative nonlinear Schrödinger model, revealing a new coupling constant and enabling spectrum analysis.

Contribution

It introduces a novel application of QISM to the quantum DNLS model, deriving all commutation relations, eigenstates, and conserved quantities explicitly.

Findings

Exact Bethe eigenstates obtained

Quantum Hamiltonian with a new coupling constant

Spectrum generated for full coupling range

Abstract

By using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated with an integrable derivative nonlinear Schrodinger (DNLS) model. From these commutation relations we obtain the exact Bethe eigenstates for the quantum conserved quantities of DNLS model. We also explicitly construct the first few quantum conserved quantities including the Hamiltonian in terms of the basic field operators of this model. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This fact allows us to apply QISM to generate the spectrum of quantum DNLS Hamiltonian for the full range of its coupling constant.