The Lieb-Schultz-Mattis-type filling constraints in the 1651 magnetic space groups

TL;DR

This paper systematically studies filling constraints in magnetic space groups, establishing conditions for trivial insulators and improving existing bounds, which aids in the search for exotic magnetic materials.

Contribution

It provides the first comprehensive analysis of filling constraints in magnetic space groups and refines the bounds for trivial insulators.

Findings

Improved the value of $m^{ ext{M}}$ for magnetic space groups.

Proved the tightness of filling constraints for most magnetic space groups.

Offers insights for discovering exotic magnetic materials with fractionalization.

Abstract

We present the first systematic study of the filling constraints to realize a `trivial' insulator symmetric under magnetic space group $\mathcal{M}$. The filling $\nu$ must be an integer multiple of $m^{\mathcal{M}}$ to avoid spontaneous symmetry breaking or fractionalization in gapped phases. We improve the value of $m^{\mathcal{M}}$ in the literature and prove the tightness of the constraint for the majority of magnetic space groups. The result may shed light on the material search of exotic magnets with fractionalization.