I want to use ITensor to obtain thermal states for the 1D Fermi-Hubbard model using the purification method and to do so I need to define an entangler Hamiltonian but I'm having some problems.

Right now I'm trying to use autoMPO to create the Hamiltonian and that requires me to define the operator |1 - N*up*i - N*dn*i'| acting on a site i and its ancilla i' (as in Eq. 26 and 29 of https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.045137 ). It seems that this operator just projects away the states |Up Up> and |Dn Dn> so I could define a tensor with two indices going and two going in out that does that(with something like to "Op.set()..." I imagine) but is there a way to use this new tensor with the autoMPO system?

If that is not possible then what would be the best way to construct the Hamiltonian MPO?