An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase

TL;DR

This paper introduces an extended Hubbard model on a Kagome lattice with ring exchange, demonstrating how it can host non-Abelian topological phases with anyonic excitations related to SU(2) Chern-Simons theory.

Contribution

It proposes a specific extended Hubbard model with ring exchange that can realize non-Abelian topological order through an exactly solvable point and perturbative analysis.

Findings

Identifies an exactly solvable point with a degenerate ground state manifold.

Shows the model can host non-Abelian topological phases near special parameter values.

Connects the model's topological order to SU(2) Chern-Simons theory.

Abstract

We propose an extended Hubbard model on a 2D Kagome lattice with an additional ring-exchange term. The particles can be either bosons or spinless fermions . At a special filling fraction of 1/6 the model is analyzed in the lowest non-vanishing order of perturbation theory. Such ``undoped'' model is closely related to the Quantum Dimer Model. We show how to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'', a necessary precondition for for a certain type of non-Abelian topological order. Near the ``special'' values, $d = 2 \cos \pi/(k+2)$, this space is expected to collapse to a stable topological phase with anyonic excitations closely related to SU(2) Chern-Simons theory at level k.