Metal-insulator transition and local moments in a narrow band: A simple thermodynamic theory

A theory of metal-insulator transition (MIT) and of the localized moments in a narrow band is given both at temperature $T=0$ and T≠0. In this approach the ratio η of doubly occupied sites is expanded in a power-expansion parameter of the ground-state energy. The coefficients of the expansion are determined from known expressions for the energy and η in certain limiting situations, while the optimal value of η is found by minimizing the energy (at $T=0$) or the free energy (T≠0). At $T=0$ the present theory reproduces the results for η and the energy obtained with the Gutzwiller method. Also, we decompose the system into localized moments and the Fermi liquid, and provide a precise meaning to the former. At T≠0 a simple expression for the entropy is proposed which contains both fermionic and localized-moment parts, each with an appropriate weighting factor. The entropy reproduces correctly both the metallic and paramagnetic-insulator limits. The coefficient γ of the linear electronic specific heat is found to be strongly enhanced close to the MIT. Additionally, we show that the insulating system (at $T=0$) behaves at T≠0 as a semiconductor with a Mott-Hubbard band gap. Our theory is based on the single-site approximation; in this paper only the paramagnetic phase is analyzed.