# Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study

## TL;DR

This study uses large-scale quantum Monte Carlo simulations to explore how interactions affect the topological properties of quadrupole insulators, revealing a transition to an antiferromagnetic phase with unique critical behavior.

## Contribution

First application of Green's function formalism in interacting quadrupole insulators, demonstrating stability against weak interactions and identifying a new universality class for the phase transition.

## Key findings

- Quadrupole insulator remains topologically stable under weak interactions.
- Strong interactions induce a continuous transition to an antiferromagnetic insulator.
- Critical exponents suggest a new universality class distinct from known AFM transitions.

## Abstract

The quadrupole insulator, a high-order topological insulator, with on-site Hubbard interaction is numerically studied by large-scale projector quantum Monte Carlo (PQMC) simulations. The Green's function formalism is successfully used to characterize topological properties in interacting quadrupole insulators for the first time. We find that the topological quadrupole insulator is stable against weak interactions and turns into a trivial antiferromagnetic (AFM) insulator by a continuous topological phase transition (TPT) for strong interactions. The critical exponents related to the TPT are estimated to be $\nu=0.67(4)$, $\beta=0.40(2)$, which are distinct from those of the known AFM transitions and suggest a new universality class.