Engineering Yang-Lee anyons via Majorana bound states

TL;DR

This paper proposes a platform using Majorana bound states in topological superconductors to realize Yang-Lee anyons, non-unitary non-Abelian anyons with potential applications in quantum computation.

Contribution

It introduces a non-Hermitian Majorana system that simulates Yang-Lee edge singularity and details a scheme for their fusion, measurement, and braiding.

Findings

Successfully estimates the central charge of the system.

Demonstrates realization of Yang-Lee edge criticality.

Provides a feasible scheme for Yang-Lee anyon manipulation.

Abstract

We propose the platform of a Yang-Lee anyon system which is constructed from Majorana bound states in topological superconductors. Yang-Lee anyons, described by the non-unitary conformal field theory with the central charge $c=-22/5$, are non-unitary counterparts of Fibonacci anyons, obeying the same fusion rule, but exhibiting non-unitary non-Abelian braiding statistics. We consider a topological superconductor junction system coupled with dissipative electron baths, which realizes a non-Hermitian interacting Majorana system. Numerically estimating the central charge, we examine the condition that the non-Hermitian Majorana system can simulate the Ising spin model of the Yang-Lee edge singularity, and confirm that, by controlling model parameters in a feasible way, the Yang-Lee edge criticality is realized. On the basis of this scenario, we present the scheme for the fusion, measurement and braiding of Yang-Lee anyons in our proposed setup.