Regularization of a strong-weak duality between pointlike interactions in one dimension

TL;DR

This paper introduces a new regularization method for pointlike interactions in 1D bosonic and fermionic systems that maintains the strong-weak duality, enabling perturbative analysis in models like Lieb-Liniger.

Contribution

It presents a novel regularization preserving the duality between bosonic and fermionic pointlike interactions, unlike previous methods.

Findings

Regularization preserves the strong-weak duality.

Enables perturbative use of duality in 1D models.

Illustrated in the Lieb-Liniger model at strong coupling.

Abstract

Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong-weak duality since the coupling constants in the bosonic and fermionic cases are inversely proportional to each other. We present a regularization of these pointlike interactions that preserves the strong-weak duality, contrary to previously known regularizations. This is proven rigorously. This allows one to use this duality perturbatively and we illustrate it in the Lieb-Liniger model at strong coupling.