Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram of the Kane-Mele model with Hubbard interactions, revealing the robustness of quantum spin liquids and the effects of interactions on edge states in quantum spin-Hall insulators.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the Kane-Mele-Hubbard model, highlighting the stability of spin liquids and the impact of interactions on edge states.

Findings

Quantum spin-liquid state is robust against weak spin-orbit coupling.

Beyond a critical U, magnetic order emerges from both phases.

Hubbard interactions suppress edge charge currents but preserve helical edge signatures.

Abstract

We consider the Kane-Mele model with spin-orbit coupling supplemented by a Hubbard U term. On the basis of projective auxiliary field quantum Monte Carlo simulations on lattice sizes up to 15 x 15, we map out the phase diagram. The quantum spin-liquid state found in the Hubbard model is shown to be robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U > U_c both states are unstable toward magnetic ordering. Within the quantum spin-Hall state we study the spin, charge and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on the edge of a ribbon. The Hubbard interaction greatly suppresses charge currents along the edge, promotes edge magnetism, but leaves the single-particle signatures of the helical liquid intact.