Exactly solvable Kondo lattice model

TL;DR

This paper presents an exact solution to a Kondo lattice model, revealing its thermodynamics, ground states, and a metal-insulator transition at half-filling, with explicit solutions in the strong coupling limit.

Contribution

The work provides the first exact thermodynamic and ground state solutions for a Kondo lattice model in the thermodynamic limit, including a detailed analysis of phase transitions.

Findings

Exact thermodynamics and ground state energies obtained.

Demonstration of a metal-insulator transition at half-filling.

Explicit solutions for strong coupling limit with resonating-valence-bond wavefunctions.

Abstract

In this work, we exactly solve a Kondo lattice model in the thermodynamic limit. The system consists of an electronic conduction band described by unconstrained hopping matrix elements between the lattice sites. The conducting electrons interact with a localized impurity spin at each lattice cell. We have found the exact thermodynamics, the ground state energies of the system. At T=0, we explicitly demonstrate that the system exhibits a metal-insulator phase transition at half-filling. In the limit of strong coupling between the impurity spin and the electrons, J=\infty, we have solved the system on a lattice of any size L. The ground states are the resonating-valence-bond type Jastrow product wavefunctions. Various correlation functions may be computed for the impurity spins, and for the singlets formed by the electrons and impurities.