Po's general LSM constraint conjecture for crystallographic lattices

Let a crystallographic group $G$ act on a lattice, and let a symmetric short-range-entangled phase (sym-SRE phase) mean a phase preserving the symmetry and having no intrinsic long-range entanglement. The lattice may be smoothly deformed by lattice homotopy, which preserves its anomaly, and a trivial lattice is one smoothly deformable to a configuration with no obstruction to a sym-SRE phase. Po's general LSM constraint conjecture. A sym-SRE phase is possible only when the lattice is smoothly deformable to a trivial lattice. This conjecture generalizes Lieb–Schultz–Mattis-type anomaly constraints to general crystallographic groups; the source presents it as a conjectural criterion for when symmetric short-range-entangled phases can occur.