An elementary proof of 1D LSM theorems.

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.