Twisted dualities and the 2d Majorana checkerboard

Large ensembles of bound Majorana modes can form their own strongly-interacting phases of matter. For example, a square lattice of Majoranas coupled purely by four-fermion plaquette terms may be the effective description for the vortex lattice on the surface of certain 3d topological insulators. This talk leverages recently formulated exact dualities to derive novel representations of such a 2d Majorana checkerboard. Some connections to quantum cellular automata (QCA) and subsystem symmetry protected topological order (SSPT) are also discussed.