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Magnetic fingerprints of fractal spectra and the duality of Hofstadter models
 

Summary: Magnetic fingerprints of fractal spectra and the
duality of Hofstadter models
O Gat and J E Avron
Department of Physics, Technion, 32000, Haifa, Israel
E-mail: omri@physics.technion.ac.il and
avron@physics.technion.ac.il
New Journal of Physics 5 (2003) 44.1­44.8 (http://www.njp.org/)
Received 5 February 2003
Published 12 May 2003
Abstract. We study the de Haas­van Alphen oscillations in the magnetization of
the Hofstadter model. Near a split band the magnetization is a rapidly oscillating
function of the Fermi energy with lip-shaped envelopes. For generic magnetic
fieldsthisstructureappearsonallscalesandprovidesathermodynamicfingerprint
of the fractal properties of the model. The analysis applies equally well to the
two dual interpretations of the Hofstadter model and the nature of the duality
transformation is elucidated.
TheHofstadtermodel[1]describesnon-interacting(spinless)electronsmovingintheplaneunder
the combined action of a magnetic field and a periodic potential. The model is a paradigm for
quantum systems with singular continuous spectra [2, 3], Chern numbers in the integer quantum
Hall effect [4], fractal quantum phase diagrams [5], quantum integrable models [6] and non-

  

Source: Avron, Joseph - Physics Department, Technion, Israel Institute of Technology

 

Collections: Physics