# 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.

## Key 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.