Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model

TL;DR

This study uses quantum Monte Carlo simulations to explore higher-order topological phases in a spin model analogous to the Benalcazar-Bernevig-Hughes electronic model, revealing new topological spin states with protected corner modes.

Contribution

It demonstrates the existence of higher-order topological spin phases in a 2D spin model and maps out the phase diagram, connecting these phases to electronic higher-order topological phases.

Findings

Identification of a valence bond solid as a higher-order topological spin phase

Detection of gapless spin modes localized at lattice corners

Mapping of the phase diagram showing the transition between phases

Abstract

We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous N\'eel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.