Emergent anyons in quantum Hall physics | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Chapters

Emergent anyons in quantum Hall physics

By Nicolas Rougerie

Appears in collection : Spectral theory of novel materials / Théorie spectrales des nouveaux matériaux

Anyons are by definition particles with quantum statistics different from those of bosons and fermions. They can occur only in low dimensions, 2D being the most relevant case for this talk. They have hitherto remained hypothetical, but there is good theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons.

I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I will argue that, under certain circumstances, these become anyons. This is made manifest by the emergence of a particular effective Hamiltonian for their motion. The latter is notoriously hard to solve even in simple cases, and well-controled simplifications are highly desirable. I will discuss a possible mean-field approximation, leading to a one-particle energy functional with self-consistent magnetic field.

Information about the video

Date of recording 19/04/2016
Date of publication 04/05/2016
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18961603
Cite this video Rougerie, Nicolas (19/04/2016). Emergent anyons in quantum Hall physics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18961603
URL https://dx.doi.org/10.24350/CIRM.V.18961603

Domain(s)

Bibliography

Arovas, D., Schrieffer, J.R., & Wilczek, F. (1984). Fractional statistics and the quantum Hall effect. Physical Review Letters, 53(7), 722-723 - http://dx.doi.org/10.1103/PhysRevLett.53.722
Cooper, N.R., & Simon, S.H. (2015). Signatures of fractional exclusion statistics in the spectroscopy of quantum Hall droplets, Physical Review Letters, 114, 106802 - http://dx.doi.org/10.1103/PhysRevLett.114.106802
Forte, S. (1991). Berry's phase, fractional statistics and the Laughlin wave function. Modern Physics Letters A, 6(34), 3152-3162 - http://dx.doi.org/10.1142/S021773239100364X
Laughlin, R.B. (1983). Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Physical Review Letters, 50(18), 1395-1398 - http://dx.doi.org/10.1103/PhysRevLett.50.1395
Laughlin, R. B. (1999). Nobel lecture: Fractional quantization. Reviews of Modern Physics, 71(4), 863-874 - http://dx.doi.org/10.1103/RevModPhys.71.863
Lundholm, D., & Solovej, J. P. (2013). Local exclusion principle for identical particles obeying intermediate and fractional statistics. Physical Review A, 88, 062106 - http://dx.doi.org/10.1103/PhysRevA.88.062106
Lundholm, D., & Solovej, J. P. (2013). Hardy and Lieb-Thirring inequalities for anyons. Communications in Mathematical Physics, 322(3), 883-908 - http://dx.doi.org/10.1007/s00220-013-1748-4
Lundholm, D., & Rougerie, N. (2015). The average field approximation for almost bosonic extended anyons. Journal of Statistical Physics, 161(5), 1236-1267 - http://dx.doi.org/10.1007/s10955-015-1382-y
Lundholm, D., & Rougerie, N. (2016). Emergence of fractional statistics for tracer particles in a Laughlin liquid. <arXiv:1601.02508> - http://arxiv.org/abs/1601.02508
Myrheim, J. (1999). Anyons. In A. Comtet, T. Jolicoeur, S. Ouvry, & F. David (Eds.), Aspects topologiques de la physique en basse dimension (pp. 265-413). Les Ulis: EDP Sciences - http://dx.doi.org/10.1007/3-540-46637-1_4
Ouvry, S. (2007). Anyons and lowest Landau level anyons. In B. Duplantier, J.-M. Raimond, & V. Rivasseau (Eds.), The Spin (pp. 77-107). Basel: Birkhäuser - http://dx.doi.org/10.1007/978-3-7643-8799-0_3
Stormer, H.L., Tsui, D.C., & Gossard, A.C. (1999). The fractional quantum Hall effect. Reviews of Modern Physics, 71(2), S298-S305 - http://dx.doi.org/10.1103/RevModPhys.71.S298
Wilczek, F. (1990). Fractional statistics and anyon superconductivity. Singapore: World Scientific - http://www.worldscientific.com/worldscibooks/10.1142/0961
Zhang, Y., Sreejith, G.J., Gemelke, N.D., & Jain, J.K. (2014). Fractional angular momentum in cold atom systems. Physical Review Letters, 113, 160404 - http://dx.doi.org/10.1103/PhysRevLett.113.160404

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2024

Give feedback