4.6 Article

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

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IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac73c4

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pointlike interaction; regularization; Lieb-Liniger model

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This article presents a regularization method for preserving the strong-weak duality of pointlike interactions, contrary to previous known regularizations. This allows perturbative use of the duality, which is illustrated in the Lieb-Liniger model at strong coupling.
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 Hermitian 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.

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