quantum Hall effect
A physical system in solid state physics consisting of electrons confined to an essentially 2-dimensional surface and subject to a perpendicular magnetic field.
In an appropriate limit of low temperature aspects of this system are described by the topological quantum field theory called Chern-Simons theory. In this limit the system has been proposed as constituting a possible implementation of topological quantum computation.
A quick review of the description via Chern-Simons theory with further pointers is in the introduction of
- Spencer D. Stirling, Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories, arXiv:0807.2857
J. Bellissard introduced an approach via noncommutative geometry and Connes-Chern character:
- J. Bellissard, A. van Elst, H. Schulz Baldes, The noncommutative geometry of the quantum Hall effect, 79 pages, J. Math. Phys. 35, 5373 (1994) cond-mat/9411052 doi
In terms of Berry phase and Chern numbers in
- Joseph E. Avron, Daniel Osadchy, Ruedi Seiler, A Topological look at the quantum Hall effect, Physics Today 56:8, doi
Relation to Pfaffian state is illuminated in
- Gregory Moore, N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. 360B(1991)362 pdf
Revised on September 27, 2013 20:39:58
by Zoran Škoda