Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

Abstract

Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States(PEPS), topological order is characterized by an entanglement symmetry of the local tensor which describes the model. This symmetry can take the form of a tensor product of group representations, or in the more general case a correlated symmetry action in the form of a Matrix Product Operator(MPO), which encompasses all string-net models. Among other things, these entanglement symmetries allow for the description of ground states and anyon excitations. Recently, the idea has been put forward to use those symmetries and the anyonic objects they describe as order parameters for probing topological phase transitions, and the applicability of this idea has been demonstrated for Abelian groups. In this paper, we extend this construction to the domain of non-Abelian models with MPO symmetries, and use it to study the breakdown of topological order in the double Fibonacci (DFib) string-net and its Galois conjugate, the non-hermitian double Yang-Lee (DYL) string-net. We start by showing how to construct topological order parameters for condensation and deconfinement of anyons using the MPO symmetries. Subsequently, we set up interpolations from the DFib and the DYL model to the trivial phase, and show that these can be mapped to certain restricted solid on solid(RSOS) models, which are equivalent to the $((5\pm \sqrt{5})/2)$-state Potts model, respectively. The known exact solutions of the statistical models allow us to locate the critical points, and to predict the critical exponents for the order parameters. We complement this by numerical study of the phase transitions, which fully confirms our theoretical predictions; remarkably, we find that both models exhibit a duality between the order parameters for condensation and deconfinement.

16 pages, 7 figures

References in corpus (10)

• Condensate induced transitions between topologically ordered phases
• Topological Order and Conformal Quantum Critical Points
• Explicit tensor network representation for the ground states of string-net models
• Topological Phase Transitions in the Golden String-Net Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Microscopic models of interacting Yang-Lee anyons
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Topological order from quantum loops and nets
• Constructing topological models by symmetrization: A PEPS study
• Quantum error correction thresholds for the universal Fibonacci Turaev-Viro code

Cited by in corpus (3)

• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Skeleton of isometric Tensor Network States for Abelian String-Net Models