Translation invariance, topology, and protection of criticality in chains of interacting anyons

Pfeifer, Robert N. C., Buerschaper, Oliver, Trebst, Simon, Ludwig, Andreas W. W., Troyer, Matthias and Vidal, Guifre (2012) Translation invariance, topology, and protection of criticality in chains of interacting anyons. Physical Review B, 86 15: 155111.1-155111.28. doi:10.1103/PhysRevB.86.155111

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Author Pfeifer, Robert N. C.
Buerschaper, Oliver
Trebst, Simon
Ludwig, Andreas W. W.
Troyer, Matthias
Vidal, Guifre
Title Translation invariance, topology, and protection of criticality in chains of interacting anyons
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2012-10-08
Sub-type Article (original research)
DOI 10.1103/PhysRevB.86.155111
Open Access Status File (Publisher version)
Volume 86
Issue 15
Start page 155111.1
End page 155111.28
Total pages 28
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2013
Language eng
Formatted abstract
Using finite-size scaling arguments, the critical properties of a chain of interacting anyons can be extracted from the low-energy spectrum of a finite system. Feiguin et al. [ Phys. Rev. Lett. 98 160409 (2007)] showed that an antiferromagnetic chain of Fibonacci anyons on a torus is in the same universality class as the tricritical Ising model and that criticality is protected by a topological symmetry. In the present paper we first review the graphical formalism for the study of anyons on the disk and demonstrate how this formalism may be consistently extended to the study of systems on surfaces of higher genus. We then employ this graphical formalism to study finite rings of interacting anyons on both the disk and the torus and show that analysis on the disk necessarily yields an energy spectrum which is a subset of that which is obtained on the torus. For a critical Hamiltonian, one may extract from this subset the scaling dimensions of the local scaling operators which respect the topological symmetry of the system. Related considerations are also shown to apply for open chains.
Keyword Quantum hall states
Non-Abelian anyons
Fractional statistics
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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Citation counts: TR Web of Science Citation Count  Cited 9 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 9 times in Scopus Article | Citations
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