PhD Thesis Defenses

Study of the phase diagram of Zn symmetric chains

In this thesis we study the phase diagrams of Zn symmetric chains. We start with investigating the topological phases of the Kitaev chain, a Z2 symmetric model, with long range couplings and a phase gradient. Then we go beyond the free fermion classification of topological phases and consider the effect of interactions by studying the Kitaev-Hubbard chain, incorporating a density-density interaction. Next we move on to the Z3 symmetric models and present a frustration free model with an exact three-fold degenerate ground state. In the end we present the phase diagram of a hopping model of Z3 Fock parafermions, the generalization of polarized Dirac fermions which could host at most two particles per site. The model has a pairwise hopping which is forbidden for fermions. In our studies we use analytical methods like the Lieb-Schultz-Mattis method, bosonization and conformal field theory, as well as numerical ones like exact diagonalization and the density matrix renormalization Group.