Lieb-Schultz-Mattis type theorems for Majorana chains with discrete symmetries

A central question in condensed matter physics is to compute the degeneracy of the ground state and decide if the excitations are gapped or gapless, given a microscopic Hamiltonian with certain local degrees of freedom. The Lieb-Schultz-Mattis theorems are (no-go) theorems that constrain the possible answers to this question. We derive a set of Lieb-Schultz-Mattis type constraints in (1+1)-dimensional spacetime relevant to the local Hamiltonians represented by Majorana fermions that are invariant under discrete symmetries.