Studies of Topology and Order in Frustrated Spin Systems
The main focus of this dissertation is the interplay between topology and order in frustrated quantum spin systems. We identify the relevant effects in the study of novel phases of matter, as they emerge in tractable quantum spin models, and we make several original contributions. In this dissertation, (a) we study quantum dimer models with frustrating interactions and holes, identifying possible phases of matter and the nature of the phase transitions between them, (b) we identify a possible mechanism of how incommensurate ordering can emerge in strongly correlated systems and show explicitly how it works in toy models of quantum frustration, such as quantum dimer models, (c) we study the quantum entanglement entropy of different topological phases in exactly solvable quantum spin models and we show explicitly how a finite correlation length affects different topological observables, and (d) we study the nature of the Mott insulator to metal transition at finite temperatures and we show that it generally belongs to the Ising universality class.
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations
University of Illinois at Urbana-Champaign