Finding a lower bound for the ground state energy

I am trying to find a way to more or less efficiently compute a lower bound for the ground state energy. I have seen but I am not aware of it, or any alternative, being implemented. Am I missing something?
How can I compute such bound?

They’re not implemented in Psi. This is an extremely niche field of research, and just skimming the paper you linked, it’s not readily implementable. (You need the expectation value of the fourth power of the Hamiltonian!) Don’t count on this changing.