Canonical strong coupling spin wave expansion of Kondo lattice magnets. I. Effective Hamiltonian via canonical transformation

TL;DR

This paper introduces a systematic strong coupling spin wave expansion for Kondo lattice magnets using a canonical transformation, revealing insights into electron-spin interactions and enabling extensions to spin-orbit coupling and pairing effects.

Contribution

It develops a novel canonical Schrieffer-Wolff transformation-based strong coupling expansion for Kondo lattice models, providing a new framework for analyzing spin wave excitations.

Findings

Transformed electron operators correspond to electrons with total spin S±1/2.

Electron degrees of freedom are described as tightly bound spin polarons.

The method can incorporate spin-orbit coupling and electron pairing effects.

Abstract

This paper develops a systematic strong coupling spin wave expansion of itinerant Kondo lattice magnets, magnets in which local moment spins are Kondo coupled to itinerant charge degrees of freedom. The strong coupling expansion is based on a canonical Schrieffer-Wolff transformation of the Hamiltonian, which is performed after $1/S$ expansion of the local moments and determined iteratively by requiring that spin-flip terms are removed at each order. We demonstrate that the canonical transformation can be viewed as an order-by-order diagonalization of the quantum Kondo coupling -- the dominant term in the strong coupling regime. A consequence is that the transformed electron operators correspond to electrons in a state of total spin $S\pm 1/2$ with the local moments, and the transformed boson operators describe spin wave excitations of the total local spin. We show that the electron degrees of freedom can be thought of as tightly bound spin polarons. We further show that the strong coupling spin wave expansion is readily extended to include the effects of spin-orbit coupling or electron pairing.