# Sublattice symmetry vs Particle hole symmetry

Sublattice symmetry and particle hole symmetry generally constrain a system's energy spectrum to be symmetric with respect to fermi level. My understanding is that they are both represented by an operator with the property $OHO^{-1}=-H$. For sublattice symmetry, $O$ is unitary and linear while for particle hole symmetry, $O$ is antinunitary and antililear. Here I have two questions:

1. Sometimes in literature, if a system's energy spectrum is symmetric with respect to fermi level, it is said to have particle hole symmetry. However, according to my understanding, this can also be attributed to sublattice symmetry. Does the term "particle hole symmetry" have some generalizations here?

2. I have never seen particle hole symmetry(in my definition) in a condensed matter system other than superconductors. Can anyone offer me an example?

Thanks!