Exactly solvable model for two-dimensional topological superconductors

Abstract

In this paper, we present an exactly solvable model for two-dimensional topological superconductors with helical Majorana edge modes protected by time-reversal symmetry. Our construction is based on the idea of decorated domain walls and makes use of the Kasteleyn orientation on a two-dimensional lattice, which was used for the construction of the symmetry protected fermion phase with ${Z}_{2}$ symmetry by Tarantino et al. and Ware et al. By decorating the time-reversal domain walls with spinful Majorana chains, we are able to construct a commuting projector Hamiltonian with zero correlation length ground state wave function that realizes a strongly interacting version of the two-dimensional topological superconductor. From our construction, it can be seen that the ${T}^{2}=\ensuremath{-}1$ transformation rule for the fermions is crucial for the existence of such a nontrivial phase; with ${T}^{2}=1$, our construction does not work.