Electron Correlation in the Hubbard Model in d{=}+∞ Dimension: Heavy Electrons in the Mott-Transition Region

The Hubbard model is studied for the Mott-transition region in the limit of high dimension d→+∞. Leading-order effects with respect to 1/d are local spin fluctuations, all of which are fully included in the single-site approximation (SSA). Because the SSA is reduced to solving the Anderson model, it is argued that a normal heavy-electron liquid forms through the Kondo effect. The Fermi-liquid relations are proven within the SSA. The other leading-order effects are mean fields of magnetism caused by exchange interaction. Therefore it depends on the competition between the Kondo effect and the exchange interaction which the ground state is, magnetic or paramagnetic. However, any other effect is a higher-order effect. The 1/d expansion from the heavy-electron liquid in the SSA is one of the most useful methods in examining lower-temperature phases in the real dimension.