Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction

The Kondo lattice model (KLM) describes a manybody system of two distinct types of degrees of freedom, itinerant electrons and localized spins which are arranged on a regular lattice. This model can be considered as an extension of the single impurity Kondo model where electrons interact with a single localized spin. The Hamiltonian of the KLM consists of two parts, the kinetic energy of the itinerant conduction electrons and the local exchange interaction between electron spin Sc and localized spin Sf, both spin 1/2 degrees of freedom, HKLM = −t X h i,ji X s (c † cjs + c † cis) + J X i † †