Rigorous analysis of the effects of electron-phonon interactions on magnetic properties in the one-electron Kondo lattice model

TL;DR

This paper rigorously analyzes how electron-phonon interactions influence the magnetic properties of the one-electron Kondo lattice model, providing new insights into ground state stability and effective Hamiltonians.

Contribution

It derives the effective Hamiltonian in the strong coupling limit and proves the magnetization theorem for the model at finite temperatures.

Findings

Magnetic properties of the ground state are rigorously characterized.

Effective Hamiltonian in the strong coupling limit is derived.

Magnetization theorem holds at finite temperatures for the effective model.

Abstract

The Kondo lattice model (KLM) is a typical model describing heavy fermion systems. In this paper, we consider the interaction of phonons with the system described by the one-electron KLM. Magnetic properties of the ground state of this model are revealed in a rigorous form. Furthermore, we derive the effective Hamiltonian in the strong coupling limit ($J\to \infty$) for the strength of the spin-exchange interaction $J$; we examine the magnetic properties of the ground state of the effective Hamiltonian and prove that the Aizenman--Lieb theorem concerning the magnetization holds for the effective Hamiltonian at finite temperatures. Generalizing the obtained results, we clarify a mechanism for the stability of magnetic properties of the ground state in the one-electron KLM system.