QLunch: Dyonic zero-energy modes

Speaker: Michele Burrello from NBI

Title: Dyonic zero-energy modes

One-dimensional systems with topological order are intimately related to the appearance of zero- energy modes localized on their boundaries.

The most common example is the Kitaev chain, which displays Majorana zero-energy modes and it is characterized by a two-fold ground state degeneracy related to the global Z_2 symmetry associated with fermionic parity. By extending the symmetry to the Z_N group, it is possible to engineer systems hosting different topological modes called parafermions.

In this talk, I will introduce one-dimensional systems with a generic discrete symmetry group G. I will define a ladder model of gauge fluxes, inspired by lattice gauge theories, that generalizes the Ising and Potts models and displays a symmetry broken phase. Through a non-Abelian Jordan-Wigner transformation, I will map this flux ladder into a model of dyonic operators, defined by the group elements and irreducible representations of G. I will show that the so-obtained dyonic model has topological order, with zero-energy modes localized at its boundary.