Mott-Hubbard Transition versus Anderson Localization in Correlated Electron Systems with Disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged (”typical”) local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.

Figure 1

Nonmagnetic ground state phase diagram of the Anderson-Hubbard model at half filling as calculated by DMFT with the typical local density of states.

Figure 2

LDOS as a function of disorder $\Delta$ for various values of the interaction $U$. Solid (dashed) curves correspond to the geometrically (arithmetically) averaged LDOS.

Figure 3

Geometrically averaged LDOS as a function of interaction $U$ for different disorder strengths $\Delta$. Solid (dashed) curves with closed (open) symbols are obtained with an initial metallic (insulating) hybridization function. Triangles: $\Delta =1$; dots: $\Delta =2.5$. Left inset: LDOS with Mott gap at $U=3$ for different disorder strengths $\Delta$. Right inset: integrated LDOS $N_{\mathrm{g}\mathrm{e}\mathrm{o}\mathrm{m}}$ as a function of $\Delta$ at $U=3$.

Figure 4

LDOS for $U=1.25$ (left column) and $U=1.75$ (right column) for different disorder strengths $\Delta$. Solid (dashed) curves correspond to the geometrically (arithmetically) averaged LDOS.