Anyon braiding and the renormalization group

TL;DR

This paper introduces a real-space renormalization group approach based on anyon braiding operations, illustrating how it leads to quantum scaling limits and connections to conformal field theories, with implications for topological quantum computing.

Contribution

It develops a novel renormalization group framework for anyonic chains using braiding, linking it to conformal field theory and quantum simulation.

Findings

Renormalization group flow for anyonic chains defined by braiding operations.

Quantum scaling limit of the Ising chain yields the Ising CFT vacuum state.

Distinguishing braiding from its inverse relates to Ising CFT chiral sectors.

Abstract

A braiding operation defines a real-space renormalization group for anyonic chains. The resulting renormalization group flow can be used to define a quantum scaling limit by operator-algebraic renormalization. It is illustrated how this works for the Ising chain, also known as transverse-field Ising model. In this case, the quantum scaling limit results in the vacuum state of the well-known Ising CFT. Distinguishing between the braiding and its inverse is directly related to the chiral sectors of the Ising CFT. This has direct implications for the simulation of CFTs on topological quantum computers.