3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators

TL;DR

This paper presents a method to engineer multi-body interactions from two-body couplings in spin systems, enabling the realization of fractional Chern insulators with abelian and non-abelian anyons, including Fibonacci anyons for universal quantum computation.

Contribution

The authors introduce a novel approach to generate higher-order interactions from two-body couplings in spin-1/2 systems, facilitating the creation of topologically ordered states with non-abelian anyons.

Findings

Engineered local 3- and 4-body interactions from two-body couplings.

Realized fractional Chern insulators with Fibonacci anyons.

Proposed implementation using qubit circuits for quantum computation.

Abstract

We describe a method for engineering local $k+1$-body interactions ($k=1,2,3$) from two-body couplings in spin-${1}{2}$ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit abelian and non-abelian anyon excitations. The most complex of these, with $k=3$, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model up to small corrections, and further, we describe the process by which one might create and manipulate non-abelian vortices in these circuits, allowing for direct control of the system's quantum information content.