TY - JOUR
T1 - Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
JF - Science Advances
JO - Sci Adv
DO - 10.1126/sciadv.1500197
VL - 1
IS - 6
SP - e1500197
AU - Levinsen, Jesper
AU - Massignan, Pietro
AU - Bruun, Georg M.
AU - Parish, Meera M.
Y1 - 2015/07/01
UR - http://advances.sciencemag.org/content/1/6/e1500197.abstract
N2 - 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.
ER -