COUPLED WIRE CONSTRUCTION OF NON-ABELIAN CHIRAL SPIN LIQUIDS
This event is part of the PhD Final Oral Exams.
Dissertation Committee: Claudio Chamon, Andrei Ruckenstein, Anatoli Polkovnikov, Emanuel Katz, Michael El-Batanouny
Topologically ordered states of matter have attracted much interest in the past decade. The search for emergent point-like non-Abelian anyons electronic systems is one of the most exciting problems in condensed matter physics, since it opens many possibilities for topological quantum computing. In this talk, I will construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the con- struction can use either quantum wires or quantum spin chains as building blocks, with the same end result. Hence, the resulting non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal eld theories (CFT) in (1 + 1)-dimensional space and time. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c < 1.