Proof of completeness of the local conserved quantities in the one-dimensional Hubbard model

TL;DR

This paper rigorously proves that all local conserved quantities in the one-dimensional Hubbard model are uniquely determined and are fully characterized by the transfer matrix expansion.

Contribution

It establishes the completeness and uniqueness of local conserved quantities in the 1D Hubbard model, confirming they are generated by the transfer matrix expansion.

Findings

Local conserved quantities are uniquely determined for each locality.

The set of local conserved quantities is complete and exhausts all possibilities.

They are generated from the expansion of the transfer matrix.

Abstract

We rigorously prove that the local conserved quantities in the one-dimensional Hubbard model are uniquely determined for each locality up to the freedom to add lower-order ones. From this, we can conclude that the local conserved quantities are exhausted by those obtained from the expansion of the transfer matrix.