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

TL;DR

This paper numerically investigates parafermion zero modes in 2D topological states, identifying signatures like topological entanglement entropy shifts and analyzing their stability, advancing understanding for experimental realization.

Contribution

It provides the first large-scale numerical study of PFZMs in FQH states and FCIs, highlighting their signatures and stability using DMRG methods.

Findings

Topological entanglement entropy shifts by a quantized amount across PFZMs

PFZMs are stable against certain perturbations in FQH and FCI systems

Numerical evidence supports potential experimental detection of PFZMs

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.