Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals

Haruki Watanabe, Hoi Chun Po, Ashvin Vishwanath, And Michael Zaleteld

Research output: Contribution to journalArticlepeer-review

132 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)14551-14556
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number47
StatePublished - Nov 24 2015

All Science Journal Classification (ASJC) codes

  • General


  • Hastings-Oshikawa-Lieb-Schultz-Mattis theorem
  • Nonperturbative arguments
  • Nonsymmorphic space groups
  • Quantum spin liquids
  • Spin-orbit coupling


Dive into the research topics of 'Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals'. Together they form a unique fingerprint.

Cite this