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

Abstract

A theory of metal-insulator transition (MIT) and of the localized moments in a narrow band is given both at temperature $T=0\mathrm{}$ and $T\ne 0$. In this approach the ratio $\eta$ 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 $\eta$ in certain limiting situations, while the optimal value of $\eta$ is found by minimizing the energy (at $T=0\mathrm{}$) or the free energy ($T\ne 0$). At $T=0\mathrm{}$ the present theory reproduces the results for $\eta$ 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 $T\ne 0$ 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 $\gamma$ of the linear electronic specific heat is found to be strongly enhanced close to the MIT. Additionally, we show that the insulating system (at $T=0\mathrm{}$) behaves at $T\ne 0$ 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.