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arXiv · 1204.4728

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

F. F. Assaad·M. Bercx·M. Hohenadler
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Abstract

The adiabatic insertion of a \pi flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that \pi 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 \pi flux 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. \pi 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. Due to the freedom to create almost arbitrary spin lattices, correlated topological insulators with \pi fluxes represent a novel kind of quantum simulator potentially useful for numerical simulations and experiments.

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F. F. Assaad, M. Bercx, M. Hohenadler. 2012-04-20. Topological Invariant and Quantum Spin Models from Magnetic \pi\ Fluxes in Correlated Topological Insulators. https://doi.org/10.1103/physrevx.3.011015

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