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

We investigate the boson-fermion duality relation for the case of quantum integrable derivative $δ$-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 $δ$-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.