Global symmetries of quantum Hall systems: lattice description

Abstract

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.

14 pages, 3 ps figures included

References in corpus (4)

• Distribution of occupation numbers in finite Fermi-systems and role of interaction in chaos and thermalization
• Electric field scaling at a B=0 metal-insulator transition in two dimensions
• A different view of the quantum Hall plateau-to-plateau transitions
• Reflection symmetry at a B=0 metal-insulator transition in two dimensions

Cited by in corpus (6)

• Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
• Effects of dissipation on quantum phase transitions
• Particle-vortex symmetric liquid
• Reflection Symmetry and Quantized Hall Resistivity near Quantum Hall Transition
• Network of edge states: random Josephson junction array description
• Modular Symmetry and Fractional Charges in N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect