Rigorous results on the ferromagnetism and metal-insulator transition of the Anderson lattice at quarter filling

We show exactly that the ground state of the Anderson lattice with U={∞} is ferromagnetic at quarter filling if the level of localized electrons sf is deep enough: εf{{{ε}}}fc$, where ${{{ε}}}fc$ is of the order of the bandwidth. Rigorous arguments show that if ${{{ε}}}fεfc, the ground state has the total spin S=(N-1)/2 for Nₑ=N+1 and S=Nₑ/2 for Nₑ{≤}N, where N is the number of lattice sites and Nₑ is that of electrons. At quarter filling, this indicates that a transition to an insulating magnetically ordered ground state will occur for a value of εf less than εfc. We observe this transition for finite U if -εf is sufficiently large.