On the Singularities at the Metal-Insulator Transitions. I : The Coherent Potential Approximation in the 50-50 Binary Alloys

概要

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Generally, the ground state energy of a many-electron system may have some singularities as a function of the coupling constant. Such a singularity is sometimes associated with a metal-insulator transition. The only case known is the discontinuity of the second derivative at the Brinkman-Rice transition which is derived in the Hubbard model by the Gutzwiller approximation. The critical exponent in this case is 2. In this paper, the value 7/2 is analytically derived for the critical exponent of the metal-insulator transition lead by CPA, where the level separation of two components of the binary alloy plays the role of the coupling constant. The sign of the additional term to the energy of the metallic phase turns out to be positive in this model while it is negative in the Gutzwiller approximation.
理論物理学刊行会の論文
1980-04-25