Jack on a Devil’s Staircase

  • Andrea Di Gioacchino
  • Marco Gherardi
  • Luca Guido MolinariEmail author
  • Pietro Rotondo
Conference paper


We review a simple mechanism for the formation of plateaux in the fractional quantum Hall effect. It arises from a map of the microscopic Hamiltonian in the thin torus limit to a lattice gas model, solved by Hubbard. The map suggests a Devil’s staircase pattern, and explains the observed asymmetries in the widths. Each plateau is a new ground state of the system: a periodic Slater state in the thin torus limit. We provide the unitary operator that maps such limit states to the full, effective ground states with same filling fraction. These Jack polynomials generalise Laughlin’s ansatz, and are exact eigenstates of the Laplace-Beltrami operator. Why are Jacks sitting on the Devil’s staircase? This is yet an intriguing problem. Talk given in Milan, Congresso di Dipartimento 2017 (L.G.M.).


Quantum Hall effect Laughlin ansatz Jack polynomials Laplace Beltrami operator 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Andrea Di Gioacchino
    • 1
  • Marco Gherardi
    • 1
  • Luca Guido Molinari
    • 1
    Email author
  • Pietro Rotondo
    • 2
  1. 1.Dipartimento di FisicaUniversità degli Studi di Milano and I.N.F.N. sezione di MilanoMilanItaly
  2. 2.University of NottinghamNottinghamUK

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