Spin liquids, exotic phases and phase transitions

Abstract

Spin liquid, or featureless Mott-Insulator, is a theoretical state of matter firstly motivated from study on High-Tc superconductor. The most striking property of spin liquids is that they do not break any physical symmetry, yet there are many types of them, meaning a phase transition is necessary from one spin liquid to another. It was a long debate about whether these exotic states can serve as the ground states in real materials or even models. In this thesis I firstly discuss a large-N model, where we show the spin liquid states can be the ground states. Because the spin liquid phases cannot be characterized by symmetry breaking, the phase transitions associated with them are naturally beyond the traditional Laudau's paradigm. I discuss a few scenarios of these exotic phase transitions to show a general picture about what can happen for such exotic transitions. Those exotic phase transitions can actually serve as a way to detect these exotic phases. Then I move to a much more realistic model: spin-1/2 Kagome lattice, where we propose a U(1)-Dirac spin liquid as the ground state. The implications on the recent material ZnCu3(OH)6C12 are discussed. Finally, I come back to the high-Tc problem. A doped spin liquid can naturally be superconducting whose many properties have already been confirmed by experiments. Here I particularly study one experimental puzzle: the nodal-antinodal dichotomy in underdoped High-Tc material. This used to be one difficulty of the doped spin liquid theory. We show that a doped spin liquid can naturally has nodal-antinodal dichotomy due to further neighbor hoppings (t' and t").