Microscopic Theory of the Quantum Hall Hierarchy

E. J. Bergholtz, T. H. Hansson, M. Hermanns, and A. Karlhede
Phys. Rev. Lett. 99, 256803 – Published 19 December 2007

Abstract

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.

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  • Received 17 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.256803

©2007 American Physical Society

Authors & Affiliations

E. J. Bergholtz, T. H. Hansson, M. Hermanns, and A. Karlhede

  • Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

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Issue

Vol. 99, Iss. 25 — 21 December 2007

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