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 ${\mathit{s}}_{\mathit{f}}$ is deep enough: ${\mathrm{\varepsilon }}_{\mathit{f}}$<${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$, where ${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$ is of the order of the bandwidth. Rigorous arguments show that if ${\mathrm{\varepsilon }}_{\mathit{f}}$<${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$, the ground state has the total spin S=(N-1)/2 for ${\mathit{N}}_{\mathit{e}}$=N+1 and S=${\mathit{N}}_{\mathit{e}}$/2 for ${\mathit{N}}_{\mathit{e}}$≤N, where N is the number of lattice sites and ${\mathit{N}}_{\mathit{e}}$ 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 ${\mathrm{\varepsilon }}_{\mathit{f}}$ less than ${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$. We observe this transition for finite U if -${\mathrm{\varepsilon }}_{\mathit{f}}$ is sufficiently large.