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A Short Introduction to Fibonacci Anyon Models
Open accessAbstract
We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial (“identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the “golden chain”, a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian SU(2)k statistics. The k→∞ limit of the latter yields ordinary SU(2) spin chains.
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Cited by
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
Mong, R. S. K., Clarke, D. J., Alicea, J., Lindner, N. H., Fendley, P., Nayak, C., Oreg, Y., Stern, A., Berg, E., Shtengel, K., et al. (2014) · Physical Review X · doi:10.1103/physrevx.4.011036 · Cited by 366
From Luttinger liquid to non-Abelian quantum Hall states
Teo, J. C. Y., & Kane, C. L. (2014) · Physical Review B · doi:10.1103/physrevb.89.085101 · Cited by 261
Guedes, T. L. M., Mena Marugán, G. A., Müller, M., & Vidotto, F. (2025) · Physical Review D · doi:10.1103/hjdk-kdhk · Cited by 5
Phases of interacting Fibonacci anyons on a ladder at half-filling
Kirchner, N., Moessner, R., Pollmann, F., & Gammon-Smith, A. (2026) · Physical Review B · doi:10.1103/c92g-mhly
Metadata
- Authors
- Trebst, S., Troyer, M., Wang, Z., & Ludwig, A. W. W.
- Venue
- Progress of Theoretical Physics Supplement
- Publisher
- Oxford University Press (OUP)
- Published
- 2008
- Volume
- 176
- Pages
- 384-407
- ISSN
- 0375-9687 (ISSN-L)
- OpenAlex
- W2037812500
- Cited by
- 162
- References
- 0
- FWCI
- 3.87
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Trebst, S., Troyer, M., Wang, Z., & Ludwig, A. W. W. (2008). A Short Introduction to Fibonacci Anyon Models. Progress of Theoretical Physics Supplement. https://doi.org/10.1143/ptps.176.384
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