Proof of the absence of local conserved quantities in the Holstein model

TL;DR

This paper proves that the one-dimensional Holstein model and the Holstein--Hubbard model lack nontrivial local conserved quantities, advancing understanding of nonintegrability in electron-phonon systems.

Contribution

It provides the first concrete proof of nonintegrability in electron-phonon coupled systems by showing the absence of local conserved quantities beyond trivial ones.

Findings

Holstein model has no nontrivial local conserved quantities besides Hamiltonian and total fermion number.

The absence of nontrivial local conserved quantities also applies to the Holstein--Hubbard model.

This expands nonintegrability proofs to systems with mixed particle statistics.

Abstract

Absence of local conserved quantities, or \textit{nonintegrability}, is often assumed when discussing various phenomena in quantum many-body systems, such as thermalization and transport. However, no concrete proof of this property is known in electron--phonon coupled systems, a typical setting for condensed matter physics. In this paper, we show that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. We further show that the absence of nontrivial local conserved quantities also holds for the more general Holstein--Hubbard model. Our result has accomplished an advance in nonintegrability proofs by expanding their scope to systems in which particles with different statistical properties are mixed.