title: Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential.
abstract: 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 Pascal'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.
authors.affiliation: Aarhus Institute of Advanced Studies, Aarhus University, DK-8000 Aarhus C, Denmark. ; School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia.
authors.forename: Jesper
authors.initials: J
authors.lastname: Levinsen
authors.affiliation: ICFO-The Institute of Photonic Sciences, 08860 Castelldefels (Barcelona), Spain.
authors.forename: Pietro
authors.initials: P
authors.lastname: Massignan
authors.affiliation: Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark.
authors.forename: Georg M
authors.initials: GM
authors.lastname: Bruun
authors.affiliation: School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia. ; London Centre for Nanotechnology, Gordon Street, London WC1H 0AH, UK.
authors.forename: Meera M
authors.initials: MM
authors.lastname: Parish
keywords: Tonks-Girardeau gas; crossover from few- to many-body physics; exact solutions; one-dimensional systems; orthogonality catastrophe; quantum many-body physics; quantum technologies; strongly correlated fermions