Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study

TL;DR

This study investigates a generalized Kane-Mele-Hubbard model with third-neighbor hopping, revealing how interactions influence the topological phase boundary using Quantum Monte Carlo and Green's function methods.

Contribution

It introduces a combined QMC and Green's function approach to analyze topological phase transitions in an interacting model with third-neighbor hopping, providing new insights into phase boundary shifts.

Findings

Interactions extend the topological phase region.

Quantum fluctuations cause boundary shifts.

Green's function features aid in identifying phase transitions.

Abstract

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector Quantum Monte Carlo (QMC) method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction-dependence of the Z2 topological insulator/trivial insulator phase boundary by calculating the Z2 invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum {\deg}uctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.