Data di Pubblicazione:
2018
Citazione:
Jack on a Devil’s Staircase / A. Di Gioacchino, M. Gherardi, L.G. Molinari, P. Rotondo - In: Toward a Science Campus in Milan : A Snapshot of Current Research at the Physics Department Aldo Pontremoli / [a cura di] P.F. Bortignon, G. Lodato, E. Meroni, M.G.A. Paris, L. Perini, A. Vicini. - Prima edizione. - [s.l] : Springer Nature Switzerland, 2018. - ISBN 9783030016289. - pp. 193-207 (( convegno Toward a Science Campus in Milan tenutosi a Milano nel 2017 [10.1007/978-3-030-01629-6_16].
Abstract:
We review a simple mechanism for the formation of plateaux in the fractional quantum Hall effect. It arises from a map of the microscopic Hamilto- nian 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.).
Tipologia IRIS:
03 - Contributo in volume
Keywords:
Quantum Hall effect; Laughlin ansatz; Jack polynomials; Laplace Beltrami operator
Elenco autori:
A. Di Gioacchino, M. Gherardi, L.G. Molinari, P. Rotondo
Link alla scheda completa:
Titolo del libro:
Toward a Science Campus in Milan : A Snapshot of Current Research at the Physics Department Aldo Pontremoli