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

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

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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

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