Non-Existence of Local Integrals of Motion in the Multi-Deformed Ising Model

TL;DR

This paper confirms that the multi-deformed Ising model lacks local integrals of motion, demonstrating non-integrability when deformed with energy and spin operators, using fermionic representations.

Contribution

It provides a proof of non-integrability for the multi-deformed Ising model with combined energy and spin perturbations.

Findings

No local integrals of motion exist beyond the trivial in the deformed model.

The fermionic representation confirms the non-integrability.

Deformations with both energy and spin operators break integrability.

Abstract

We confirm the non-integrability of the multi-deformed Ising Model, an already expected result. After deforming with the energy operator $\phi_{1,3}$ we use the Majorana free fermionic representation for the massive theory to show that, besides the trivial one, no local integrals of motion can be built in the theory arising from perturbing with both energy and spin operators.