# Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu = 1/2 + 1/2$ Bilayers

## TL;DR

This paper introduces a variational matrix product state ansatz to model the continuous transition from Abelian to non-Abelian topological phases in bosonic bilayer fractional quantum Hall systems, with implications for experimental realization.

## Contribution

It presents a novel variational ansatz capturing the entire transition physics and proposes engineering tunneling to create Majorana modes at interfaces.

## Key findings

- The transition is continuous and involves decoupling of antisymmetric modes.
- Identifies tunneling strength for observing non-Abelian statistics.
- Proposes creating and characterizing Majorana modes at engineered interfaces.

## Abstract

We propose a one-parameter variational ansatz to describe the tunneling-driven Abelian to non-Abelian transition in bosonic $\nu=1/2+1/2$ fractional quantum Hall bilayers. This ansatz, based on exact matrix product states, captures the low-energy physics all along the transition and allows to probe its characteristic features. The transition is continuous, characterized by the decoupling of antisymmetric degrees of freedom. We futhermore determine the tunneling strength above which non-Abelian statistics should be observed experimentally. Finally, we propose to engineer the inter-layer tunneling to create an interface trapping a neutral chiral Majorana. We microscopically characterize such an interface using a slightly modified model wavefunction.