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

TL;DR

This paper shows how inserting luxes into correlated topological insulators reveals localized states and enables the construction of quantum spin models, offering a new approach for simulations and experimental studies.

Contribution

It introduces a method using luxes in quantum Monte Carlo to identify and study correlated topological insulators and their spin models.

Findings

luxes induce localized spin and charge states in topological insulators.

Correlations lead to tunable magnetic excitons mediating spin interactions.

lux-based models can simulate complex quantum spin systems.

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.