Exactly Solvable Model for Two Dimensional Topological Superconductor

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.

7 pages

References in corpus (3)

• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory

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• Anomalous symmetry protected topological states in interacting fermion systems
• A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States
• Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Enforced symmetry breaking by invertible topological order
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Commuting projector models for (3+1)d topological superconductors via string net of (1+1)d topological superconductors
• Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases