Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field

TL;DR

This paper rigorously proves that the spin-1/2 XYZ chain with a magnetic field lacks local conserved quantities, showing that all conserved operators are nonlocal and supported on large contiguous regions.

Contribution

It provides a rigorous proof that the XYZ chain with magnetic field has no local conserved quantities, clarifying the nature of conserved operators in this model.

Findings

No local conserved quantities in the XYZ chain with magnetic field

Any conserved quantity is supported on at least half of the system

The absence of local conserved quantities is rigorously established

Abstract

We rigorously prove that the spin-1/2 XYZ chain with a magnetic field has no local conserved quantity. Any nontrivial conserved quantity of this model is shown to be a sum of operators supported by contiguous sites with at least half of the entire system. We establish that the absence of local conserved quantity in concrete models is provable in a rigorous form.