Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators

Abstract

The adiabatic insertion of a π flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that π fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_{2} topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a π flux gives rise to a Kramers doublet of spin-fluxon states with a Curie-law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spin fluxons. π fluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Because of the freedom to create almost arbitrary spin lattices, correlated topological insulators with π fluxes represent a novel kind of quantum simulator, potentially useful for numerical simulations and experiments.