Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-05-29
Physics
Condensed Matter
Strongly Correlated Electrons
Completely rewritten and greatly extended. Includes an introduction to diagrammatic representation of anyons on surfaces of ar
Scientific paper
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 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, this subset always corresponds to the scaling dimensions of local scaling operators which respect the topological symmetry of the system. Related considerations are also shown to apply for open chains.
Pfeifer Robert N. C.
Vidal Guifre
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