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

Abstract

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 Z_2 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.

12 pages, 12 figures, published version

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Cited by in corpus (11)

• Correlation effects in two-dimensional topological insulators
• Phase diagram of the Kane-Mele-Coulomb model
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings
• Topological flat bands in optical checkerboard-like lattices
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Nature of continuous phase transitions in interacting topological insulators
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Bandwidth controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations