Gauge symmetry and non-Abelian topological sectors in a geometrically constrained model on the honeycomb lattice.
Physical review. E, Statistical, nonlinear, and soft matter physics 75:5 Pt 1 (2007) 051120
Abstract:
We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.Topological Entanglement Entropy from the Holographic Partition Function
Journal of Statistical Physics Springer Nature 126:6 (2007) 1111-1144
Cooper pairs and exclusion statistics from coupled free-fermion chains
Journal of Statistical Mechanics Theory and Experiment IOP Publishing 2007:02 (2007) p02017-p02017
Edge states and tunneling of non-Abelian quasiparticles in the ν=5∕2 quantum Hall state and p+ip superconductors
Physical Review B American Physical Society (APS) 75:4 (2007) 045317
Loop models and their critical points
Journal of Physics A: Mathematical and Theoretical IOP Publishing 39:50 (2006) 15445