Topological Phase Transitions in the Golden String-Net Model

TL;DR

This paper investigates the phase diagram of a Fibonacci anyon string-net model, identifying various topological and trivial phases separated by different types of quantum phase transitions, including second-order and first-order, with unusual critical behavior.

Contribution

It combines high-order series expansions and exact diagonalizations to precisely locate phase boundaries and characterize the universality classes of transitions in a non-Abelian topological model.

Findings

Identification of second-order quantum critical points separating topological and trivial phases.

Discovery of a first-order transition with infinite ground-state degeneracy.

Evidence of unusual universality classes at critical points.

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.