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

Robert N C Pfeifer*, Oliver Buerschaper, Simon Trebst, Andreas W W Ludwig, Matthias Troyer, Guifre Vidal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 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.

Original languageEnglish
Article number155111
Pages (from-to)1-28
Number of pages28
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number15
Publication statusPublished - 8 Oct 2012
Externally publishedYes


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