Dartmouth Events

Title: "Fractionalized Electrons in Second Quantization"

Abstract: Quasiparticles that carry fractional charge have been extensively
investigated in a static approximation where they appear attached to
frozen topological deffects. Key examples are the Laughlin wave functions
of the fractional quantum Hall effect for the first approach, and the
Jackiw-Rebbi or Su-Schrieffer-Heeger model for the second. In this talk I
introduce an ansatz for the second quantization operators of
quasiparticles of fractional charge that can emerge in systems of
fermions. If the fermions that are being fractionalized carry non-Abelian
quantum numbers, then the ansatz fractionalizes the electric charge of the
fermions, but not their non-Abelian charges. There always exists a local
transformation that maps the initial set of fractionally charged
quasiparticles into a new set carrying definite values of both
fractionalized electric and non-fractionalized non-Abelian charges. To
provide an application I study numerically the zero-energy modes at the
interface between a normal (non-fractionalizing) and a fractional
topological superconductor.