Topological Phase Transitions in the Golden String-Net Model

Abstract

We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes.

7 pages, 4 figures, published version

References in corpus (8)

• Condensate induced transitions between topologically ordered phases
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Adiabatic Preparation of Topological Order
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Space-Time Geometry of Topological phases
• Wilson Line Picture of Levin-Wen Partition Functions
• Topological order from quantum loops and nets

Cited by in corpus (1)

• The Kitaev-Ising model, Transition between topological and ferromagnetic order