Ising Anyons in Frustration-Free Majorana-Dimer Models

TL;DR

This paper introduces Majorana-dimer models that combine bosonic dimers with Majorana modes, realizing a fermionic phase with non-Abelian anyons and a gapped edge, exactly solvable in frustration-free systems.

Contribution

The authors present new Majorana-dimer models that realize an Ising topological phase combined with a p_x - ip_y superconductor, including explicit Hamiltonians and analysis of their topological properties.

Findings

Realization of an Ising ot(p_x - ip_y) phase in Majorana-dimer models

Exactly solvable, frustration-free Hamiltonians constructed for these phases

Ground-state properties match predictions of the combined topological theories

Abstract

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.