Fermionic dual of one-dimensional bosonic particles with derivative delta function potential

TL;DR

This paper explores the duality between bosonic and fermionic systems with derivative delta-function interactions in one dimension, revealing a fermionic system with inverse coupling related to the bosonic one.

Contribution

It introduces a dual fermionic model for a derivative delta-function bosonic gas, detailing how the fermionic coupling relates inversely to the bosonic coupling and eigenfunction momentum.

Findings

Derived the dual fermionic system with zero-range interaction

Established the inverse relationship between fermionic and bosonic coupling constants

Analyzed the simplest case of two particles with derivative delta interaction

Abstract

We investigate the boson-fermion duality relation for the case of quantum integrable derivative $\delta$-function bose gas. In particular, we find out a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative $\delta$-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the centre-of-mass momentum of the corresponding eigenfunction.