Collective states of interacting Fibonacci anyons.
We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry end points we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.
Trebst
Simon
S
Microsoft Research, Station Q, University of California-Santa Barbara, CA 93106, USA.
Ardonne
Eddy
E
Feiguin
Adrian
A
Huse
David A
DA
Ludwig
Andreas W W
AW
Troyer
Matthias
M