Edge Modes of Zn Symmetric Chains

Sammanfattning: In this Licentiate Thesis we will study the topological phases of Z2 and Z3 symmetric chains.We will present the Kitaev chain, a Z2 symmetric model of spinless fermions, and obtain allthe eigenstates of the model with an open boundary condition which hosts Majorana zeromodes in the topological phase. We will also present zero modes of the Kitaev chain withphase gradient in the pairing term and longer range couplings. This model could hostMajorana zero modes as well as a 'one-sided' zero energy fermionic state. We will study therole of interactions on the topological phase by considering a special model for which one canobtain the ground states exactly. Similarly, for the Z3 case, we will present a 3-state clockmodel as well as a solvable model for which the ground states are obtained exactly. We willbriefly address the presence of edge modes in these models as well.