Duality between weak and strong interactions in quantum gases

TL;DR

This paper introduces a novel duality connecting strongly interacting bosons to weakly interacting fermions in 1D quantum gases, enabling new analytical approaches to study these systems.

Contribution

It proposes a new regularization of fermionic interactions that makes perturbation theory applicable to strongly interacting bosons, solving a longstanding problem.

Findings

Derived a weak fermionic potential suitable for perturbation theory

Computed the finite temperature spectral function of the Cheon-Shigehara model

Established a duality linking Lieb-Liniger bosons to fermionic models

Abstract

In one dimensional quantum gases there is a well known "duality" between hard core bosons and non-interacting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long standing problem. Our derivation relies on regularizing the only point-like interaction between fermions in 1D that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularisations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model.