Exotic, Topological, and Many Body Localized Quantum Phase Transitions

In this thesis we will study recent examples of exotic, topological, and many body localized quantum phase transitions. In Chapter 2 we study the quantum phase transition between the Z_2 spin liquid and valence bond solid (VBS) orders on a triangular lattice. We find a possible nematic Z_2 spin liquid intermediate phase and predict a continuous 3d XY* transition to the neighboring columnar and resonating-plaquette VBS phases. In Chapter 3 we demonstrate that an extended Kane-Mele Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin S^z conservation and the previously mentioned strongly interacting fully gapped phase. We argue that the first quantum phase transition is related to the Z_16 classification of the topological superconductor ^3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O(4) nonlinear sigma model field theory with a Theta-term. In Chapter 4 we propose that if the highest and lowest energy eigenstates of a Hamiltonian belong to different SPT phases, then this Hamiltonian can't be fully many body localized. In Chapter 5 we study the disordered XYZ spin chain and its marginally many body localized critical lines, which we find to be characterized by an effective central charge c'=ln2 and continuously varying critical exponents