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.

- Wikipedia,
*Quantum Hall effect*,*Fractional quantum Hall effect*

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

- Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, (arXiv:0707.1888)

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.