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Résumé |
We compute the mod-2 cohomology rings 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 Z2. 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. |
