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A Chern-Simons effective field theory for the Pfaffian quantum Hall state
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Abstract We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU (2) 2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU (2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.
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Cites
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
Cited by
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Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1083 · Cited by 6,861
Self-citationMajorana zero modes and topological quantum computation
Sarma, S. D., Freedman, M., & Nayak, C. (2015) · npj Quantum Information · doi:10.1038/npjqi.2015.1 · Cited by 1,180
Self-citationSato, M., & Fujimoto, S. (2009) · Physical Review B · doi:10.1103/physrevb.79.094504 · Cited by 597
Read, N. (2009) · Physical Review B · doi:10.1103/physrevb.79.045308 · Cited by 454
Particle-Hole Symmetry and theν=52Quantum Hall State
Lee, S.-S., Ryu, S., Nayak, C., & Fisher, M. P. A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.236807 · Cited by 414
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Metadata
- Authors
- Fradkin, E., Nayak, C., Tsvelik, A., & Wilczek, F.
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1998-04
- Volume
- 516
- Issue
- 3
- Pages
- 704-718
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W2031485772
- Cited by
- 245
- References
- 1
- FWCI
- 5.40
- Type
- journal article
- Language
- en
- Open access
- green
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- Fradkin, E., Nayak, C., Tsvelik, A., & Wilczek, F. (1998). A Chern-Simons effective field theory for the Pfaffian quantum Hall state. Nuclear Physics B. https://doi.org/10.1016/s0550-3213(98)00111-4
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