Forward scattering approximation and bosonization in integer quantum Hall systems

In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approxima...

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Bibliographic Details
Published in:Annals of physics 2008-03, Vol.323 (3), p.673-704
Main Authors: Rosenau da Costa, M., Westfahl, H., Caldeira, A.O.
Format: Article
Language:English
Subjects:
APPROXIMATIONS
BOSON EXPANSION
Bosonization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COLLECTIVE EXCITATIONS
DISPERSION RELATIONS
ELECTRON GAS
ELECTRONS
Forward scattering approximation
Gases
HALL EFFECT
Mathematical models
ONE-DIMENSIONAL CALCULATIONS
Particle physics
Quantum Hall effect
Quantum theory
SCATTERING
Spectral function
SPECTRAL FUNCTIONS
SPIN
TWO-DIMENSIONAL CALCULATIONS
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Summary:In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single-particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single-particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga–Luttinger model and the bosonization of two-dimensional electron gases.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2007.04.018