Ising Anyons in frustration-free Majorana-Dimer models: Construction and Spectrum

Dimer models have long been a fruitful playground for understanding topological physics. This talk introduces a new class—termed Majorana-dimer models—wherein bosonic dimers are decorated with pairs of Majorana modes. We show that it is possible to construct a gapped, frustration-free, and analytically tractable Majorana-dimer Hamiltonians on the triangular and Fisher lattices. By analyzing the low-energy spectrum, we establish the following properties: (1) edges are fully gapped, (2) the bulk supports deconfined Ising anyons, and (3) on a torus the system admits three-fold ground-state degeneracy. From these, we suggest that these Hamiltonians possess non-Abelian Ising topological order that generalizes the $Z_2$ topological order familiar from pure dimer models.