On the renormalization of contact interactions for the configuration-interaction method in two-dimensions

Massimo Rontani, G. Eriksson, S. Åberg, S. M. Reimann

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The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac δ-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schrödinger equation for a regularized contact interaction. We discuss here a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.

Original languageEnglish
Article number065301
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number6
Publication statusPublished - 2017 Mar 7

Subject classification (UKÄ)

  • Atom and Molecular Physics and Optics

Free keywords

  • configuration interaction method
  • degenerate Bose gases
  • degenerate Fermi gases
  • exact diagonalization
  • Fermi pseudopotential
  • few-body physics
  • two-dimensional harmonic trap

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