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.).

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].

Jack on a Devil’s Staircase

A. Di Gioacchino;M. Gherardi;L.G. Molinari
;
P. Rotondo
2018

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.).
Quantum Hall effect; Laughlin ansatz; Jack polynomials; Laplace Beltrami operator
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
2018
I.N.F.N.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/608589
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