Disorder effects in correlated topological insulators

TL;DR

This paper explores how disorder impacts the phases of two-dimensional topological insulators, using advanced numerical methods to analyze both non-interacting and interacting models, revealing model-dependent stability conditions.

Contribution

It introduces a comprehensive numerical and analytical framework to study disorder effects on topological insulators, including phase boundary determination and critical exponent calculation.

Findings

Different models show varied stability of topological phases under disorder.

The study provides critical exponents for phase transitions in non-interacting models.

An analytical theory predicts stability trends with high accuracy.

Abstract

Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both non-interacting and interacting models of two-dimensional topological insulators. In the fermion sign problem-free interacting models we study, electron-electron interactions are described by an on-site repulsive Hubbard interaction and disorder is included via the one-body hopping operators. In both the non-interacting and interacting models we make use of recent advances in highly accurate real-space numerical evaluation of topological invariants to compute phase boundaries, and in the non-interacting models determine critical exponents of the transitions. We find different models exhibit distinct stability conditions of the topological phase with respect to interactions and disorder. We provide a general analytical theory that accurately predicts these trends.