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.).File | Dimensione | Formato | |
---|---|---|---|
Proceeding_MOLINARI.pdf
accesso riservato
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
607.53 kB
Formato
Adobe PDF
|
607.53 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
DiGioacchino2018_Chapter_JackOnADevilSStaircase.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
650.9 kB
Formato
Adobe PDF
|
650.9 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.