To create @@H^2@@, you could always create @@H@@ with
AutoMPO and then use the function
nmultMPO to multiply the MPO @@H@@ with itself.
Otherwise, to use
AutoMPO, you would have to write out by hand all of the terms resulting from @@H^2@@, and input those terms into
AutoMPO. This shouldn't be too bad for a Hamiltonian with local interactions.