Designing Topological Quantum Matter: From Conformal Field Theory to Non-Abelian Topological Insulators
This event is part of the PhD Final Oral Exams.
Dissertation Committee: Claudio Chamon, Anatoli Polkovnikov, Michael El-Batanouny, So-Young Pi, Emanuel Katz
Abstract: Recent advances in experimental condensed matter physics suggest a powerful new paradigm for the realization of exotic phases of quantum matter in the laboratory. Rather than conducting an exhaustive search for materials that realize these phases at low temperatures, it may be possible to design quantum systems that exhibit the desired properties. In this talk, I will argue in favor of a theoretical approach, the coupled-wire construction, that is morally (if not historically) motivated by these developments, with an eye towards applications to topological states of matter. The goal of coupled-wire constructions is to build models of exotic quantum phases "from the ground up" by coupling together one-dimensional quantum wires. Using this method, one can design analytically tractable microscopic theories for topological states of matter starting from well-understood building blocks. As an example of this approach, I will present a coupled-wire construction in which the input, a family of conformal field theories, is understood exactly, while the output is a family of new non-Abelian topological states of matter in three spatial dimensions. The family of topological phases constructed in this way can be viewed as "non-Abelian topological insulators" that generalize the non-Abelian Read-Rezayi series of bosonic quantum Hall states to one higher spatial dimension.