Microscopic theory of the quantum Hall hierarchy

Details Microscopic theory of the quantum Hall hierarchy Microscopic theory of the quantum Hall hierarchy

2007-02-22

arxiv.org/abs/cond-mat/0702516v2

Phys. Rev. Lett. 99, 256803 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 2 figures. Published

Scientific paper

10.1103/PhysRevLett.99.256803

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 {\it 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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