Local vs non-local correlation effects in interacting quantum spin Hall insulators

TL;DR

This paper investigates how local and non-local Coulomb interactions influence the electronic properties of quantum spin-Hall insulators, revealing different regimes and phase transition behaviors depending on the bare mass term.

Contribution

It distinguishes the roles of local and non-local correlations in quantum spin-Hall insulators and characterizes their effects across different mass regimes using quantum cluster methods.

Findings

Non-local correlations dominate near the zero-mass semi-metallic line.

Local correlations lead to a first-order topological phase transition at larger masses.

Different correlation regimes are identified based on the bare mass value.

Abstract

The impact of Coulomb interaction on the electronic properties of a quantum spin-Hall insulator is studied using quantum cluster methods, disentangling local from non-local effects. We identify different regimes, according to the value of the bare mass term, characterized by drastically different self-energy contributions. For small mass, non-local correlations start to be important and eventually dominate over local ones when getting close enough to the zero-mass semi-metallic line. For intermediate and large mass, local correlation effects outweigh non-local corrections, leading to a first-order topological phase transition, in agreement with previous predictions.