nLab
quantum Hall effect

Contents

Idea

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.

References

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 non-abelian Statistics (and eventually connection to braiding, modular tensor categories, and topological quantum computing followed) was made initially in

  • Gregory Moore, N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. 360B(1991)362 pdf

For a more recent discussion of these connections see

category: physics

Last revised on August 21, 2014 at 01:13:54. See the history of this page for a list of all contributions to it.