Absence of nontrivial local conserved quantities in the Hubbard model on the two or higher dimensional hypercubic lattice

TL;DR

This paper proves that the Hubbard model on two or higher dimensional hypercubic lattices lacks nontrivial local conserved quantities, indicating non-integrability, and extends Shiraishi's proof from spin systems to fermionic models.

Contribution

It is the first to extend Shiraishi's proof of absence of conserved quantities to a fermionic Hubbard model in higher dimensions.

Findings

No nontrivial local conserved quantities in the Hubbard model for d≥2

The proof requires three steps, more than the two steps needed for spin systems

Partial determination of conserved quantities in 1D Hubbard model

Abstract

By extending the strategy developed by Shiraishi in 2019, we prove that the standard Hubbard model on the $d$-dimensional hypercubic lattice with $d\ge2$ 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 $S=\tfrac12$ quantum spin systems in two or higher dimensions; our proof requires three steps, while that of Shiraishi and Tasaki requires only two steps. It is also necessary to partially determine the conserved quantities of the one-dimensional Hubbard model to accomplish our proof.