TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.5.161
TI  - Crystallography, group cohomology, and Lieb–Schultz–Mattis constraints
PY  - 2025/05/20
UR  - https://scipost.org/SciPostPhys.18.5.161
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 5
SP  - 161
A1  - Liu, Chunxiao
AU  - Ye, Weicheng
AB  - We compute the mod-2 cohomology ring for three-dimensional (3D) space groups and establish a connection between them and the lattice structure of crystals with space group symmetry. This connection allows us to obtain a complete set of Lieb-Schultz-Mattis constraints, specifying the conditions under which a unique, symmetric, gapped ground state cannot exist in 3D lattice magnets. We associate each of these constraints with an element in the third mod-2 cohomology of the space group, when the internal symmetry acts on-site and its projective representations are classified by powers of $\mathbb{Z}_2$. We demonstrate the relevance of our results to the study of $U(1)$ quantum spin liquids on the 3D pyrochlore lattice. We determine, through anomaly matching, the symmetry fractionalization patterns of both electric and magnetic charges, extending previous results from projective symmetry group classifications.
ER  -

@Article{10.21468/SciPostPhys.18.5.161,
	title={{Crystallography, group cohomology, and Lieb–Schultz–Mattis constraints}},
	author={Chunxiao Liu and Weicheng Ye},
	journal={SciPost Phys.},
	volume={18},
	pages={161},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.5.161},
	url={https://scipost.org/10.21468/SciPostPhys.18.5.161},
}