Mott-Hubbard transition in infinite dimensions

We analyze the unanalytical structure of metal-insulator transition (MIT) in infinite dimensions. A multiple-valued structure in Green’s function and other thermodynamical quantities with respect to the interaction strength U are observed at low temperatures by introducing a transformation into the dynamical mean-field equation of Hubbard model. A complete description of stable, metastable, and unstable phases is established in the regime $U_{c1\mathrm{}}\mathrm{}\left(T\right)<U<\mathrm{}{U}_{c2\mathrm{}}\mathrm{}\left(T\right).$ The Maxwell construction is performed to evaluate the MIT line $U^{*}\mathrm{}\left(T\right).$ We show how the first-order MIT at $U^{*}\mathrm{}\left(T\right)\mathrm{}$ for $T>\mathrm{}0\mathrm{}$ evolves into the second-order one at $U_{c2\mathrm{}}\mathrm{}\left(0\right)\mathrm{}$ for $T=0.\mathrm{}$ The phase diagram near MIT is presented.