Title: Numerical Observation of Parafermion Zero Modes and their Stability in 2D Topological States,
Abstract: The possibility of realizing non-Abelian excitations (non-Abelions) in
two-dimensional (2D) Abelian states of matter has generated a lot of interest
recently. A well-known example of such non-Abelions are parafermion zeros modes
(PFZMs) which can be realized at the endpoints of the so called genons in
fractional quantum Hall (FQH) states or fractional Chern insulators (FCIs). In
this letter, we discuss some known signatures of PFZMs and also introduce some
novel ones. In particular, we show that the topological entanglement entropy
(TEE) shifts by a quantized value after crossing PFZMs. Utilizing those
signatures, we present the first large scale numerical study of PFZMs and their
stability against perturbations in both FQH states and FCIs within the
density-Matrix-Renormalization-Group (DMRG) framework. Our results can help
build a closer connection with future experiments on FQH states with genons.