Modified Gutzwiller theory of the metal-insulator transition: Application to heavy-fermion systems

The Gutzwiller and Hubbard approaches to the Hubbard Hamiltonian are each of a very different nature and lead to some qualitatively different results for certain quantities, for example, for the quasiparticle density of states as a function of the interaction divided by the bandwidth $\frac{U}{W}$. The metal-to-insulator transition occurs for the Hubbard approach at $\frac{U}{W}\simeq 1$ and for the Gutzwiller approach at $\frac{U}{W}=2\mathrm{}$. We suggest a simple modification of the Gutzwiller theory consisting of the use of a physically reasonable momentum distribution. We find the transition now occurring at $\frac{U}{W}\simeq 1$ while the spin susceptibility and compressibility remain finite. Applications to heavy-fermion systems and normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are discussed.