title: Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals.
abstract: We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator--a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an essential way and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches: The first one is an entanglement-based scheme, and the second one studies the system on an appropriate flat "Bieberbach" manifold to obtain the filling conditions for all 230 space groups. These approaches assume only time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.
authors.affiliation: Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139;
authors.forename: Haruki
authors.initials: H
authors.lastname: Watanabe
authors.affiliation: Department of Physics, University of California, Berkeley, CA 94720;
authors.forename: Hoi Chun
authors.initials: HC
authors.lastname: Po
authors.affiliation: Department of Physics, University of California, Berkeley, CA 94720; Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, CA 94720;
authors.forename: Ashvin
authors.initials: A
authors.lastname: Vishwanath
authors.affiliation: Station Q, University of California, Santa Barbara, CA 93106 mikezaletel@cnsi.ucsb.edu.
authors.forename: Michael
authors.initials: M
authors.lastname: Zaletel
keywords: Hastings–Oshikawa–Lieb–Schultz–Mattis theorem; nonperturbative arguments; nonsymmorphic space groups; quantum spin liquids; spin-orbit coupling