Coupled wire construction of a topological phase with chiral tricritical Ising edge modes

Tricritical Ising (TCI) phase transition is known to occur in several interacting spin and Majorana fermion models and is described in terms of a supersymmetric conformal field theory (CFT) with central charge $c=7/10$. The field content of this CFT is highly nontrivial and includes among its primary fields the Fibonacci anyon, making it of potential interest to strategies seeking to implement fault-tolerant topological quantum computation with non-Abelian phases of matter. In this paper we explore the possibility that a TCI CFT can occur at the edge of a gapped two-dimensional topological state as a stable phase. We discuss a possible realization of this 2D phase based on a coupled-wire construction using the Grover-Sheng-Vishwanath chain model of Majorana zero modes coupled to Ising spins which is known to undergo the TCI phase transition. From the combined analysis using mean-field theory, conformal field theory, and density matrix renormalization group (DMRG) on two- and four-leg ladders, we find that the left- and right-moving gapless TCI modes become spatially separated and reside on two opposite edges of the system, forming a precursor of the required 2D topological phase.