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The possibility of realizing non-Abelian excitations (non-Abelions) intwo-dimensional (2D) Abelian states of matter has generated a lot of interestrecently. 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 infractional quantum Hall (FQH) states or fractional Chern insulators (FCIs). Inthis letter, we discuss some known signatures of PFZMs and also introduce somenovel ones. In particular, we show that the topological entanglement entropy(TEE) shifts by a quantized value after crossing PFZMs. Utilizing thosesignatures, we present the first large scale numerical study of PFZMs and theirstability against perturbations in both FQH states and FCIs within thedensity-Matrix-Renormalization-Group (DMRG) framework. Our results can helpbuild a closer connection with future experiments on FQH states with genons.

Numerical Observation of Parafermion Zero Modes and their Stability in 2D Topological States