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Bergholtz EJ, Hansson TH, Hermanns M, et al. Microscopic theory of the quantum Hall hierarchy. Phys Rev Lett. 2007;99(25):256803doi: 10.1103/PhysRevLett.99.256803.
Bergholtz, E. J., Hansson, T. H., Hermanns, M., & Karlhede, A. (2007). Microscopic theory of the quantum Hall hierarchy. Physical review letters, 99(25), 256803. https://doi.org/10.1103/PhysRevLett.99.256803
Bergholtz, E J, et al. "Microscopic theory of the quantum Hall hierarchy." Physical review letters vol. 99,25 (2007): 256803. doi: https://doi.org/10.1103/PhysRevLett.99.256803
Bergholtz EJ, Hansson TH, Hermanns M, Karlhede A. Microscopic theory of the quantum Hall hierarchy. Phys Rev Lett. 2007 Dec 21;99(25):256803. doi: 10.1103/PhysRevLett.99.256803. Epub 2007 Dec 19. PMID: 18233544.
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Phys Rev Lett. 2007 Dec 21;99(25):256803. doi: 10.1103/PhysRevLett.99.256803. Epub 2007 Dec 19.

Microscopic theory of the quantum Hall hierarchy.

Physical review letters

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

Affiliations

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

PMID: 18233544 DOI: 10.1103/PhysRevLett.99.256803

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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