Naturally, in general, ground state preparation is QMA-complete. There exists a paper by Andrew Childs, David Gosset & Zak Webb, which shows that ground state preparation for the Bose-Hubbard model is QMA-complete.
However, is it known what the complexity of ground state preparation for the Fermi-Hubbard model is? I could not find this in the literature directly, does this follow trivially from a general result which I am missing?