RT Journal Article
SR Electronic
T1 Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP e1500197
DO 10.1126/sciadv.1500197
VO 1
IS 6
A1 Levinsen, Jesper
A1 Massignan, Pietro
A1 Bruun, Georg M.
A1 Parish, Meera M.
YR 2015
UL http://advances.sciencemag.org/content/1/6/e1500197.abstract
AB 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.