1005.5486 (Robert N. C. Pfeifer et al.)

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

Robert N. C. Pfeifer, Matthias Troyer, Guifre Vidal

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. In Phys. Rev. Lett. 98, 160409 (2007), Feiguin et al. showed that an antiferromagnetic (AFM) 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. We now study finite rings of interacting anyons on the disc as well as the torus, and show that analysis on the disc 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.

View original: http://arxiv.org/abs/1005.5486