Global symmetries of quantum Hall systems: lattice description

Details Global symmetries of quantum Hall systems: lattice description Global symmetries of quantum Hall systems: lattice description

1997-02-25

arxiv.org/abs/cond-mat/9702211v1

Phys. Rev. B56, 6810-22 (1997).

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, 3 ps figures included

Scientific paper

10.1103/PhysRevB.56.6810

I analyze non-local symmetries of finite-size Euclidean 3D lattice Chern-Simons models in the presence of an external magnetic field and non-zero average current. It is shown that under very general assumptions the particle-vortex duality interchanges the total Euclidean magnetic flux Phi/(2 Pi) and the total current I in a given direction, while the flux attachment transformation increases the flux in a given direction by the corresponding component of the current, Phi -> Phi+4 Pi I, independently of the disorder. In the language of 2+1 dimensional models, appropriate for describing quantum Hall systems, these transformations are equivalent to the symmetries of the phase diagram known as the Correspondence Laws, and the non-linear current-voltage mapping between mutually dual points, recently observed near the quantum Hall liquid-insulator transitions.

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