Interacting multi-component fermions and the Yang-Baxter equation: Future prospects

Abstract

The remarkable exact solution of 1D interacting fermions heralded a new era in the study of quantum many-body problems. The mathematical structure of the underlying Yang-Baxter equation led to profound advances in other fields. Recently there has been a significant revival of interest in 1D quantum many-body problems due to the striking and ongoing experimental developments in the study of cold quantum matter. In particular, through the trapping and cooling of interacting systems of atomic bosons and fermions in low dimensions. There is, e.g., already rather spectacular agreement between theory and experiment for 1D interacting bosons. This includes an experimental test of Yang-Yang thermodynamics for bosons on a chip...