  A one-dimensional fermionic system, such as a superconducting wire, may host
Majorana zero-energy edge modes (MZMs) at its edges when it is in the
topological phase. MZMs provide a path to realising fault-tolerant quantum
computation, and so are the focus of intense experimental and theoretical
studies. However, given a Hamiltonian, determining whether MZMs exist is a
daunting task as it relies on knowing the spectral properties of the
Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic
non-interacting model that supports MZMs and the Hamiltonian can be fully
diagonalised. However, for interacting models, the situation is far more
complex. Here we consider a different classification of models, namely, ones
with frustration-free Hamiltonians. Within this class of models, interacting
and non-interacting systems are treated on an equal footing, and we identify
exactly which Hamiltonians can realise MZMs.
