Mott-Hubbard transition in infinite dimensions

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