Commuting projector models for (3+1)d topological superconductors via string net of (1+1)d topological superconductors

Abstract

We discuss a way to construct a commuting projector Hamiltonian model for a (3+1)d topological superconductor in class DIII. The wave function is given by a sort of string net of the Kitaev wire, decorated on the time reversal (T) domain wall. Our Hamiltonian is provided on a generic 3d manifold equipped with a discrete form of the spin structure. We will see how the 3d spin structure induces a 2d spin structure (called a Kasteleyn direction on a 2d lattice) on T domain walls, which makes possible to define fluctuating Kitaev wires on them. Upon breaking the T symmetry in our model, we find the unbroken remnant of the symmetry which is defined on the time reversal domain wall. The domain wall supports the 2d non-trivial SPT protected by the unbroken symmetry, which allows us to determine the SPT classification of our model, based on the recent QFT argument by Hason, Komargodski, and Thorngren.

arXiv comment32 pages, 15 figures. v2: minor changes

References in corpus (28)

• Unpaired Majorana fermions in quantum wires
• Topological phases of fermions in one dimension
• Fermion Path Integrals And Topological Phases
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Symmetry protected topological phases from decorated domain walls
• Dai-Freed anomalies in particle physics
• Spin TQFTs and fermionic phases of matter
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Dimers on surface graphs and spin structures. II
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• On the cobordism classification of symmetry protected topological phases
• Dimers on surface graphs and spin structures. I
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• Lattice Model for Fermionic Toric Code
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Pin TQFT and Grassmann integral
• Exactly Solvable Model for Two Dimensional Topological Superconductor
• Unoriented 3d TFTs
• Diagrammatic State Sums for 2D Pin-Minus TQFTs

Cited by in corpus (3)

• Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
• Enforced symmetry breaking by invertible topological order
• Anomaly constraint on chiral central charge of (2+1)d topological order