Boundaries of Topological Phases Going Through Condensation Phase Transitions

Abstract

Motivated by experimental observation of the fractional quantum Hall effect and connections to fault-tolerant quantum computing, the study of topological phases of matter has advanced greatly over the past few decades. The abstract mathematical tools used in this field can, however, lose contact with the physical systems in question, which makes some natural questions difficult to address in that framework. This thesis describes an elementary and physically motivated construction which reveals the robust edge physics of a topological phase. The construction shows that edge degrees of freedom can be tracked through certain kinds of bulk phase transitions, called anyon condensations. In particular, the number of chiral current carrying modes at the boundary cannot change through anyon condensation. We illustrate the construction through detailed analysis of anyon condensation transitions in a non-chiral phase, the toric code, and in chiral phases, the Kitaev spin liquids.