Abstract
Ville Lahtinen (Nordita, Sweden)
Majorana fermion lattices models for interacting non-Abelian anyons
We introduce a Majorana fermion lattice model to study interacting non-Abelian anyons emerging in realistic physical systems. We apply it to Kitaev's honeycomb lattice model and show that the Abelian phases emerging due to lattices of non-Abelian Ising anyon are fully determined by the anyon-anyon interactions when both nearest and next to nearest interactions are included. The necessity to consider the next to nearest terms derives from oscillations in the interactions that have been discovered also in $p$-wave superconductors and in fractional quantum Hall liquids. Our model is thus general and applicable to any system that supports tunneling Majorana fermions.