Anyons and the quantum Hall effect - a pedagogical review

By A. Stern. 2007

314 citations recorded by the source corpus.

The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined "anyons", may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/13585f8e7f7da2092b9deaaa9dd1b517991f1637

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. J. Dalibard
2. J. Alicea
3. F. Gerbier
4. Matthew Fisher
5. P. Fendley
6. C. Nayak
7. A. Stern
8. Erez Berg

In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. J. Dalibard
3. N. Lindner
4. A. Stern
5. C. Nayak
6. P. Fendley
7. F. Gerbier
8. Roger S. K. Mong

Citations in the corpus

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, background): “The quantum Hall effect catalyzed numerous breakthroughs in the search for anyons in physical systems [18,19].”
• Topological bands for ultracold atoms (2018, unknown): “Similarly, the (gapped) particle-like excitations in the bulk of the system have fractional charge, and are predicted to have fractional quantum exchange statistics (Stern, 2008).”
• Gauge fields for ultracold atoms in optical superlattices (2009, background): “In such systems, electrons “bind” to magnetic vortices, forming strongly correlated phases with striking properties, such as exotic excitations (“anyons”) which obey fractional statistics [2].”