Berry phases for Landau Hamiltonians on deformed tori

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γθ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γθ the geodesic motion restricted to the fundamental domain of this group is chaotic.

Original languageEnglish
Pages (from-to)2792-2802
Number of pages11
JournalJournal of Mathematical Physics
Volume36
Issue number6
Publication statusPublished - 1995

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Berry Phase
Hamiltonians
Torus
Half-plane
half planes
Parameter Space
Symmetry
Fundamental Domain
symmetry
Modular Group
Negative Curvature
Discrete Group
Symmetry Group
Geodesic
Poincaré
subgroups
Subgroup
Metric
eigenvectors
Motion

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Berry phases for Landau Hamiltonians on deformed tori. / Lévay, P.

In: Journal of Mathematical Physics, Vol. 36, No. 6, 1995, p. 2792-2802.

Research output: Contribution to journalArticle

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