Duality between Weak and Strong Interactions in Quantum Gases

In one-dimensional quantum gases there is a well known duality between hard core bosons and noninteracting 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 pointlike interaction between fermions in one dimension that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularizations 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.

Automated summary

In one-dimensional quantum gases, there is a duality between hard core bosons and noninteracting fermions. However, the exact duality connecting strongly interacting bosons to weakly interacting fermions is still unknown at the field theory level. This study proposes a solution to this problem by regularizing the pointlike interaction between fermions in one dimension, which induces a discontinuity in the wave function proportional to its derivative. By introducing a weak potential for small interaction strengths, standard methods of diagrammatic perturbation theory can be applied to strongly interacting bosons.