  The Lieb-Schultz-Mattis (LSM) theorem and its descendants represent a class
of powerful no-go theorems that rule out any short-range-entangled (SRE)
symmetric ground state irrespective of the specific Hamiltonian, based only on
certain microscopic inputs such as symmetries and particle filling numbers. In
this work, we introduce and prove a new class of LSM-type theorems, where any
symmetry-allowed SRE ground state must be a symmetry-protected topological
(SPT) phase with robust gapless edge states. The key ingredient is to replace
the lattice translation symmetry in usual LSM theorems by magnetic translation
symmetry. These theorems provide new insights into numerical models and
experimental realizations of SPT phases in interacting bosons and fermions.
