By extending the strategy developed by Shiraishi in 2019, we prove that the standard Hubbard model on the d-dimensional hypercubic lattice with \(d\ge 2\) does not admit any nontrivial local conserved quantities. The theorem strongly suggests that the model is non-integrable. To our knowledge, this is the first extension of Shiraishi’s proof of the absence of conserved quantities to a fermionic model. Although our proof follows the original strategy of Shiraishi, it is essentially more subtle compared with the proof by Shiraishi and Tasaki of the corresponding theorem for \(S=\tfrac{1}{2}\) quantum spin systems in two or higher dimensions. The difficulty comes mainly from the fact that both the one-dimensional Hubbard model and the model with \(U=0\) (i.e., the free fermion) in any dimension are integrable.
