Abstract
The adiabatic insertion of a flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a flux gives rise to a Kramers doublet of spin-fluxon 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 spin fluxons. 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. Because of the freedom to create almost arbitrary spin lattices, correlated topological insulators with fluxes represent a novel kind of quantum simulator, potentially useful for numerical simulations and experiments.
5 More- Received 23 April 2012
DOI:https://doi.org/10.1103/PhysRevX.3.011015
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Published by the American Physical Society
Popular Summary
As exotic states of matter, topological insulators have, for a number of years now, commanded the fundamental interest, and fueled the scientific creativity, of a broad swath of condensed matter physicists. But, identifying these remarkable states of matter unambiguously has been fiendishly difficult. One interesting approach—a powerful one if viable—relies on the answer to the following question: Is it possible—and if yes, how—to detect unambiguously a topological insulator from its bulk properties, as opposed to from its surface properties? In this theoretical paper, we answer this question in the context of 2-dimensional (2D) topological insulators with substantial electronic interactions (thus termed “correlated topological insulators”). Our approach exploits a unique response of these systems to localized magnetic defects engineered through injections of magnetic fluxes.
In a 2D topological insulator, insertion of a magnetic flux of the size of half a flux quantum—a flux—gives rise to two types of states localized around the flux: a so-called Kramers pair of spin fluxons carrying spin and a pair of charge fluxons carrying charge . The existence of these states and their quantum numbers are intimately tied to the properties of the topological insulator, in particular, its topological invariant. Previous work on fluxes was limited to 2D topological insulators in which electronic interactions can be safely ignored. We have shown, with a paradigmatic model for correlated topological insulators, that electronic interactions remove charge fluxons from the low-energy excitation spectrum of the systems but leave spin fluxons detectable via a Curie-law-type contribution to the bulk magnetic susceptibility—a property routinely measured in condensed matter physics labs. Combining these types of theoretical predictions, which are enabled by the powerful quantum Monte Carlo computational methods and easily accessible bulk-measurement techniques, leads to a simple, yet highly effective tool for identifying 2D correlated topological insulators.
Another, but no less significant, usefulness of this approach, which we have also demonstrated, is that the creation of spin fluxons in response to magnetic fluxes opens a new route to artificially designing and simulating quantum spin models within the bulk gap of topological insulators—creative stimuli to new theoretical and experimental efforts.