Y(so(5)) symmtry of the nonlinear Schr$\ddot{o}$dinger model with four-cmponents

TL;DR

This paper demonstrates that the four-component fermionic quantum nonlinear Schrödinger model possesses a $Y(so(5))$ symmetry, with constructed Yangian generators satisfying key algebraic relations, revealing deep symmetry properties.

Contribution

It constructs explicit Yangian generators for the four-component fermionic NLS model and proves they satisfy the Drinfel'd and RTT relations, establishing $Y(so(5))$ symmetry.

Findings

Yangian generators satisfy Drinfel'd formula

Generators fulfill the RTT relation with rational R-matrix

Model exhibits $Y(so(5))$ symmetry

Abstract

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.