Exact solution for the two-site Kondo-Lattice Model - a limiting case for an insulator

TL;DR

This paper derives an exact analytical solution for a two-site Kondo-lattice model in the insulator limit, providing a benchmark for approximations and a foundation for future generalizations to more complex systems.

Contribution

It presents the first exact solution for a two-site Kondo-lattice model in the insulator case, advancing understanding of local exchange interactions in limited lattice systems.

Findings

Exact Green's function derived for the two-site insulator case

Spectral weights of energy poles explicitly calculated

Provides a benchmark for testing approximation methods

Abstract

The Kondo-lattice model is well established as a method to describe an exchange coupling between single conduction electrons and localized magnetic moments. As a nontrivial exact result the zero-bandwidth limit (atomic limit) can be used to test approximations for this model. As soon as the translational symmetry is broken (for instance by sublattice structures) it is necessary to consider more than one lattice site. Therefore, we study as a starting point for generalizations the situation of a two-site cluster. An equation-of-motion approach is chosen to obtain the one-particle Green's function. In order to determine the spectral weights of its energy poles, we derive different possibilities for the calculation of the involved correlation functions. In this paper the analytical exact result for the situation of an insulator is presented. In a forthcoming article we generalize the calculations to arbitrary electron densities, keeping as the only constraint S=1/2.