Chiral Edge States Emerging on Anyon-Net

TL;DR

This paper introduces a symmetry-based lattice model construction for non-Abelian topological phases, successfully demonstrating chiral edge states through numerical simulations, offering a new approach to study strongly coupled 2+1D systems.

Contribution

It presents a novel method leveraging modular tensor categories to realize chiral topological phases with non-Abelian anyons at the microscopic level.

Findings

Demonstrates chiral edge modes in Ising and Fibonacci anyon systems

Uses tensor network simulations to verify topological edge states

Provides a new theoretical framework for strongly coupled 2+1D topological matter

Abstract

We propose a symmetry-based approach to constructing lattice models for chiral topological phases, focusing on non-Abelian anyons. Using a 2+1D version of anyon chains and modular tensor categories(MTCs), we ensure exact MTC symmetry at the microscopic level. Numerical simulations using tensor networks demonstrate chiral edge modes for topological phases with Ising and Fibonacci anyons. Our method contrasts with conventional solvability approaches, providing a new theoretical avenue to explore strongly coupled 2+1D systems, revealing chiral edge states in non-Abelian anyonic systems.