Commuting projector models for (3 +1 )dimensional topological superconductors via a string net of (1 +1 )dimensional topological superconductors
Abstract
We discuss a way to construct a commuting projector Hamiltonian model for a (3 +1 )dimensional topological superconductor in class DIII. The wave function is given by a sort of string net of the Kitaev wire, decorated on the timereversal (T ) domain wall. Our Hamiltonian is provided on a generic threedimensional (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 it 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 timereversal domain wall. The domain wall supports the 2D nontrivial symmetryprotected topological (SPT) phase protected by the unbroken symmetry, which allows us to determine the SPT classification of our model, based on the recent quantum field theory argument by Hason, Komargodski, and Thorngren.
 Publication:

Physical Review B
 Pub Date:
 August 2020
 DOI:
 10.1103/PhysRevB.102.075135
 arXiv:
 arXiv:2006.00159
 Bibcode:
 2020PhRvB.102g5135K
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 32 pages, 15 figures. v2: minor changes