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.
Highlights
A topological insulator represents a novel state of matter characterized by a special band structure that can result, e.g., from strong spin-orbit interaction [1,2]
We have presented quantum Monte Carlo results for a correlated quantum spin Hall insulator with topological defects in the form of fluxes
Our results demonstrate that fluxes can be combined with exact numerical simulations and lead to clear signatures of nontrivial topological properties in spectral and thermodynamic properties
Summary
A topological insulator represents a novel state of matter characterized by a special band structure that can result, e.g., from strong spin-orbit interaction [1,2]. We use fluxes in combination with exact quantum Monte Carlo simulations and show that they can be used efficiently to probe the topological invariant of correlated topological insulators This method does not rely on an adiabatic connection to a noninteracting state, and it may be used for fractional states. The spins correspond to the spin fluxons created by inserting fluxes, and the interaction is mediated by magnetic excitons corresponding to collective magnetic fluctuations of the topological insulator These spin models can be studied theoretically with the quantum Monte Carlo method, or experimentally. In the absence of Rashba coupling, 1⁄4 0, the Kane-Mele model describes a Z2 quantum spin Hall insulator for any p>ffiffiffi 0 This state is characterized by a bulk band gap Ásp 1⁄4 3 3, a spin gap Ás 1⁄4 2Ásp, and a quantized spin Hall conductivity sxy e2 2.
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