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

In this talk we present a class of Kondo-Heisenberg toy models, i.e., toy models of itinerant electrons coupled to local moments, for which the ground state and low-energy excitations can be determined exactly. In particular, we consider the Kondo-Heisenberg dimer and the one-dimensional Kondo-Heisenberg chain with one electron. We compute the exact low-energy magnetic excitations of the Kondo ferromagnet in the limit of strong Kondo coupling and compare the energy and structure of these excitations with spin wave calculations based on a recently introduced spin wave expansion scheme for itinerant magnets. This spin wave expansion scheme, which we refer to as canonical spin wave theory, is designed to correctly describe the quantum nature of the local Kondo coupling. Here we show that all features of the exact solution are correctly reproduced by the spin wave expansion order-by-order in the strong coupling expansion parameters. This reveals and emphasizes that the spin wave expansion correctly captures the quantum nature of the spin waves in itinerant magnets. In a broader sense, the toy models considered here powerfully highlight the fundamental difference between itinerant Kondo lattice ferromagnets and Heisenberg ferromagnets. Whereas in a Heisenberg ferromagnet the spin wave excitations are exact eigenstates of the Hamiltonian, this is not the case for a Kondo ferromagnet. Our work elucidated how well spin wave theory approximates the exact magnetic excitations.