Non-Abelian fusion rules from Abelian systems with SPT phases and graph topological order

Abstract

Since Ref. [1] shows the emergence of non-Abelian fusion rules in some examples of a class of Abelian models, but does not prove whether these rules also exist in other cases, the purpose of this paper is to present such proof emphasizing the importance of the existence of these rules. By the way, as the ground state of these models can be degenerate as a function of their algebra and, hence, they can support some symmetry-protected topological (SPT) phases, we prove that these non-Abelian fusion rules are always necessary for these SPT phase transitions to occur via a condensation mechanism or/and some global symmetry breaking.

20 pages, 2 figures; 3 tables; published in Annals of Physics

References in corpus (6)

• Fault-tolerant quantum computation by anyons
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Braid Topologies for Quantum Computation
• Topological Order from a Cohomological and Higher Gauge Theory perspective
• Coulomb interactions, Dirac sea polarization and $SU(4)$ symmetry breaking of the integer quantum Hall states of graphene
• Non-Abelian Fusion Rules from an Abelian System

Cited by in corpus (2)

• Finite-group gauge theories on lattices as Hamiltonian systems with constraints
• Quantum Double Models coupled to matter fields: a detailed review for a dualization procedure