Simplifying quantum double Hamiltonians using perturbative gadgets

TL;DR

This paper introduces perturbative gadgets tailored for simulating non-abelian anyonic Hamiltonians, simplifying the realization of Kitaev's quantum double models through low-energy effective Hamiltonians.

Contribution

It extends perturbative gadget techniques to non-abelian anyonic systems, providing a simplified construction for quantum double Hamiltonians.

Findings

Effective low-energy Hamiltonian approximates non-abelian anyonic models

Simplifies realization of Kitaev's quantum double Hamiltonians

Perturbative analysis of hopping-term Hamiltonian

Abstract

Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.