Exactly Solvable Model for Two Dimensional Topological Superconductor

TL;DR

This paper introduces an exactly solvable model for a two-dimensional topological superconductor with protected helical Majorana edge modes, utilizing decorated domain walls and Kasteleyn orientation to realize a strongly interacting phase.

Contribution

It presents a novel exactly solvable model for 2D topological superconductors with time reversal symmetry, employing decorated domain walls and a commuting projector Hamiltonian.

Findings

Constructed a zero correlation length ground state wave function.

Demonstrated the importance of T^2=-1 for the nontrivial phase.

Provided a framework for strongly interacting 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 $Z_2$ symmetry in Ref. \onlinecite{Tarantino2016,Ware2016}. 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.