%0 Journal Article
%A Levinsen, Jesper
%A Massignan, Pietro
%A Bruun, Georg M.
%A Parish, Meera M.
%T Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
%D 2015
%R 10.1126/sciadv.1500197
%J Science Advances
%P e1500197
%V 1
%N 6
%X A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascalâ€™s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.
%U https://advances.sciencemag.org/content/advances/1/6/e1500197.full.pdf