Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

See allHide authors and affiliations

Science Advances  24 Jul 2015:
Vol. 1, no. 6, e1500197
DOI: 10.1126/sciadv.1500197


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.

  • quantum many-body physics
  • one-dimensional systems
  • strongly correlated fermions
  • Tonks-Girardeau gas
  • exact solutions
  • orthogonality catastrophe
  • quantum technologies
  • crossover from few- to many-body physics

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

View Full Text

Stay Connected to Science Advances