| I this talk, I will argue that the proximity of a 1D quantum wire to an s-wave superconductor (SC) and a ferro-magnet (FM) with an in-plane magnetic order can realize the (1+1)d sine-Gordon model. Using a conformal field theory(CFT) approach, I will discuss the phase diagram of this model, and will show that the sine-Gordon model is critical at its self-dual point with a second order phase transition expected. The universality class of this phase transition is that of the Q-state Potts model (Z parafermion CFT), where Q is determined by the unperturbed Hamiltonian. I will argue that at the domain wall between SC and FM induced regions, "parafermion zero modes" are expected. I will also derive their quantum dimensions and their non-Abelian braid statistics. Finally, I will discuss the physical realizations of these systems. |
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