Exact results for the Spectra of Bosons and Fermions with Contact Interaction

Stefan Mashkevich 1, Sergey I. Matveenko 2, Stéphane Ouvry 3

Nuclear Physics B 763 (2007) 431-444

An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.

  • 1. Schrodinger,
  • 2. Landau Institute for Theoretical Physics,
    Landau Institute for Theoretical Physics
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud