Realizing discontinuous wave functions perturbatively
Abstract
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 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 CheonShigehara model, the fermionic model dual to the celebrated LiebLiniger model.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.08626
 Bibcode:
 2021arXiv210908626G
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases
 EPrint:
 5 pages + supplemental material