Exactly solvable model for two-dimensional topological superconductors

Abstract

In this paper, we present an exactly solvable model for two dimensional topological superconductor 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 Z2 symmetry in Ref. 1 and 2. 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 = −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.

Commuting-projector Hamiltonians for two-dimensional topological insulators: Edge physics and many-body invariants

“…We briefly review the exactly solvable model for Tinvariant 2D topological superconductors introduced in Ref. [13]; our commuting-projector Hamiltonian for 2D topological insulators naturally extends this model as we will see in Sec. II C. For brevity and ease of generalization to CP-protected topological phases, throughout the main text we focus on models constructed on the honeycomb lattice.…”

“…(i) As in Ref. [13], let "long edges" denote Fisher-lattice edges derived from the original honeycomb lattice. Moreover, label the two honeycomb sublattices by A and B [colored red and green, respectively, in Fig.…”

“…The topological-superconductor construction presented in Ref. [13], along with our topological-insulator generalization, implicitly assume that the manifold on which the models are defined is orientable. In this section, we first discuss how to adapt these models to a Klein bottle manifold in a CPsymmetric manner.…”

“…We will show that decorating Ising-spin domain walls with two Kitaev chains [12] in a time-reversal-symmetric and particle-conserving manner (instead of a single Kitaev chain as done in Ref. [13]) allows one to construct commutingprojector models for T -symmetric topological insulators. Our model, though strongly interacting, possesses the same symmetry and edge properties of band-theoretic quantum spin Hall insulators.…”

“…The rest of the paper is organized as follows. Section II briefly reviews the commuting-projector model for T -invariant topological superconductors [13] and then generalizes the construction to 2D topological insulators. Sections III and IV explore gapped and gapless edge phases in our commuting-projector topological-insulator Hamiltonians, demonstrating consistency with band-theoretic phenomenology for weakly interacting topological insulators.…”