# Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling

## TL;DR

This paper demonstrates that edge potentials can induce topological phase transitions between Pfaffian and anti-Pfaffian states in half-filled quantum Hall systems, highlighting the significance of edge effects in experimental observations.

## Contribution

It reveals that edge potentials alone can drive topological phase transitions in quantum Hall systems at half-filling, supported by analytical and numerical evidence.

## Key findings

- Edge potentials can switch between Pfaffian and anti-Pfaffian phases.
- Particle-hole conjugation of Hamiltonians is equivalent to tuning edge potentials.
- Edge effects are crucial in understanding experimental phases in quantum Hall systems.

## Abstract

We show that in quantum Hall systems at half-filling, edge potentials alone can drive transitions between the Pfaffian and anti-Pfaffian topological phases. We conjecture this is true in realistic systems even in the presence of weak bulk interactions that break the particle-hole symmetry. The strong effects of edge potentials could be understood from different topological shifts of competing phases, manifested on the disk geometry as the variation of orbital numbers at fixed number of particles. In particular, we show analytically particle-hole conjugation of Hamiltonians on the disk is equivalent to the tuning of edge potentials, which allows us to explicitly demonstrate the phase transition numerically. The importance of edge potentials in various experimental contexts, including the recently discovered particle-hole symmetric phase is also discussed.