Kaleidoscope of topological phases with multiple Majorana species

TL;DR

This paper explores a square-octagon Kitaev model variant that exhibits a rich topological phase diagram with multiple Majorana species, characterized by various Chern numbers, supporting different types of anyonic excitations.

Contribution

It introduces a new exactly solvable lattice model with a diverse set of topological phases and Majorana modes, expanding understanding of topological quantum states.

Findings

Multiple topological phases with Chern numbers from 0 to ±4.

Support for localized Majorana modes in certain phases.

Identification of phases with Ising and SU(2)_2 anyon theories.

Abstract

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some of them exhibiting the localized Majorana fermions that feature in proposals for topological quantum computing. The Chern invariant $\nu$ is one important characterization of such phases. Here we look at the square-octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and enjoys a rich phase diagram featuring distinct abelian and nonabelian phases with $\nu= 0,\pm1,\pm2,\pm3$ and $ \pm4$. The $\nu=\pm1 $ and $\nu=\pm3$ phases all support localized Majorana modes and are examples of Ising and $SU(2)_2$ anyon theories respectively.