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

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The adiabatic insertion of a πflux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that πfluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z₂ topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a πflux gives rise to a Kramers doublet of spinon 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 spinons. πfluxes 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. Due to the freedom to create almost arbitrary spin lattices, correlated topological insulators with πfluxes represent a novel kind of quantum simulator potentially useful for numerical simulations and experiments.