Fibonacci topological phase in arrays of anyonic chains

Fibonacci anyon, an exotic quasi-particle excitation, plays a pivotal role in realization of a quantum computer. Starting from a SU (2)(4) topological phase, in this paper we demonstrate a way to construct a Fibonacci topological phase which has only one non-trivial excitation described by the Fibonacci anyon. We show that arrays of anyonic chains created by excitations of the SU(2)(4) phase leads to the Fibonacci phase. We further demonstrate that our theoretical propositions can be extended to other topological phases.