Valence fluctuations and electric reconstruction in the extended Anderson model on the two-dimensional Penrose lattice

We study the extended Anderson model on the two-dimensional Penrose lattice, combining the real-space dynamical mean-field theory with the noncrossing approximation. It is found that the Coulomb repulsion between localized and conduction electrons does not induce a valence transition, but the crossover between the Kondo and mixed valence states is in contrast to the conventional periodic system. In the mixed-valence region close to the crossover, nontrivial valence distributions appear, characteristic of the Penrose lattice, demonstrating that the mixed-valence state coexists with local Kondo states in certain sites. The electric reconstruction in the mixed valence region is also addressed.

Figure 1

Penrose lattice with $N=4181$.

Figure 2

DOS for the $f$ electrons (a) and conduction electrons (b) in the noninteracting system with ${\epsilon }_f=0$ and $V/t=0.5$. Panel (c) represents the corresponding integrated DOS.

Figure 3

Distribution of the number of $f$ electrons (a) and valence susceptibility (b) as functions of the energy of the $f$ level in the system with $N=1591$ at temperature $T/t=0.2$ when $U_{cf}/t=0$, 16, and 36.

Figure 4

Density plot of the standard deviation for the valence $n^f$ in the system with $T/t=0.2$ and $N=1591$. The dashed line represents the crossover between the Kondo and mixed valence regions.

Figure 5

(a) The number of $f$ electrons as a function of the temperature $T/t$ when ${\epsilon }_f/t=-5, U_{cf}/t=10$, and $N=4181$. (b) and (c) show the cross sections of the valence distribution at $T/t=10$ and 1. (d) and (e) show the cross sections at low temperatures with $Z=5$ and $Z=4$, respectively.

Figure 6

(a) Classification of vertices in the Penrose lattice. The number represents the coordination number for each vertex. Detailed classification of vertices with $Z=5$ (b) and $Z=4$ (c).

Figure 7

Profiles of the quantity ${log}_{10}{I}_{\mathbf{k}}$ in the system $(N=4181)$ with ${\epsilon }_f/t=-5$ and $U_{cf}/t=10$ when $T/t=0.2$ (left panel) and $T/t=1.0$ (right panel).