Kondo-Heisenberg toy models: Comparison of exact results and spin wave expansion

TL;DR

This paper compares exact solutions and spin wave approximations for one-dimensional Kondo-Heisenberg models, demonstrating that the strong coupling $1/S$ spin wave expansion accurately captures low-energy excitations and provides insights into Kondo magnetism.

Contribution

It introduces a strong coupling $1/S$ spin wave expansion for Kondo-Heisenberg models and validates its accuracy against exact solutions, clarifying the nature of magnetic excitations.

Findings

Spin wave energies match exact solutions order-by-order.

Electron operators correspond to spin polaron states.

Insights into differences between itinerant and localized Kondo magnets.

Abstract

In this paper we study a class of exactly solvable Kondo-Heisenberg toy models in one dimension, with the goal of comparing the exact low-energy excitations of the ferromagnetic ground state to the approximate solution obtained from spin wave theory. In doing so we employ a recently introduced strong coupling $1/S$ spin wave expansion, which effectively describes excitations of the total spin $S\pm 1/2$ on a given site (i.e., sum of local moment and electron spin). We further make use of the fact that the ground state of Kondo lattice models with quantum spins and a single electron is a ferromagnet, and that the magnetic excitations of the ferromagnet can be exactly determined. We demonstrate that the energies and eigenstates of the spin waves are in full agreement with the exact solution order-by-order in $1/S$ and $t/J_K$, the strong coupling expansion parameter. In the specific case of antiferromagnetic Kondo coupling, when the exact ground state wave function describes spin polaron, we show that the electron operators of the spin wave formalism precisely correspond to the spin polaron states. More broadly, the study of Kondo-Heisenberg toy models is shown to provide insight into the fundamental distinction between itinerant Kondo magnets and Heisenberg magnets.