  The Lieb-Schultz-Mattis (LSM) theorem and its generalizations forbids the
existence of a unique gapped ground state in the presence of certain lattice
and internal symmetries and thus imposes powerful constraints on the low energy
properties of quantum many-body systems. We provide an elementary proof of a
class of generalized LSM theorems in 1D using matrix product state
representations and the representation theory of groups.
