Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice

TL;DR

This paper proves that the quantum compass model on a square lattice has no local conserved quantities other than its Hamiltonian, using an extension of Shiraishi's method.

Contribution

It establishes a rigorous proof that the quantum compass model lacks nontrivial local conserved quantities, advancing understanding of its integrability properties.

Findings

No nontrivial local conserved quantities in the model

Extension of Shiraishi's method to this model

Clarifies the model's non-integrability

Abstract

By extending the method developed by Shiraishi, we prove that the quantum compass model on the square lattice does not possess any local conserved quantities except for the Hamiltonian itself.