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Title:
Duality in Quantum Hall compressible states
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Abstract:
It has long been known empirically that quantum Hall plateau transitions enjoy an apparent self-duality symmetry manifest in that the current-voltage (I-V) curves are nonlinear and are symmetric around their liner behavior at the quantum phase transition. This behavior was first observed in dirtier samples and is now know to occur in the compressible states at filling fractions 1/2 and 1/4. This empirical result was interpreted by Shimshoni, Sondhi and Shahar (PRB 55, 13730 (1997)) as a manifestation of a particle-vortex duality. Yet, the origin of this symmetry has been mysterious and has remained unexplained until quite recently. In a recent paper (Hart Goldman and Eduardo Fradkin, PRB 98, 165137 (2018)) we used the recently developed dualities of Dirac fermions (D. T. Son Phys. Rev X. 5, 031027 (2015); N. Seiberg, T. Senthil, C. Wang and E. Witten, Ann. Phys. 374, 3095 (2016)) to show that the mirror symmetry of the Jain sequences converging on 1/2n compressible states explain the observed self-duality as a property of the compressible states.
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