Scaling between periodic Anderson and Kondo lattice models

Continuous-time quantum Monte Carlo method combined with dynamical mean field theory is used to calculate both periodic Anderson model (PAM) and Kondo lattice model (KLM). Different parameter sets of both models are connected by the Schrieffer-Wolff transformation. For degeneracy $N=2$, a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction $U$ for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the $f$ electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRh${\text{In}}_5$ in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value.

Figure 1

Density of $f$-electron states obtained from the solution of the periodic Anderson model for the values of Hubbard $U=3,6,9$.

Figure 2

Conduction electron density of states obtained from the solution of the periodic Anderson model for the values of Hubbard $U=3,6,9$. Also shown the result obtained from the Kondo lattice simulation.

Figure 3

Conduction electron self-energy of the periodic Anderson model with $N=2$ calculated for several values of $U$ and the conduction electron self-energy of the Kondo lattice model that corresponds to $U\to \infty$ limit.

Figure 4

The convergence for the $f$-electron self-energy obtained from the periodic Anderson model with $N=2$ upon increase in the interaction $U$. The limiting behavior of this quantity extracted from the solution of the Kondo lattice model is also plotted.

Figure 5

Comparison between quasiparticle residues $z_f$ calculated as a function of Hubbard $U$ using periodic Anderson model with $N=2$, Kondo lattice model as well as a slave-boson method described in Ref. 48.

Figure 6

Calculated using the periodic Anderson model with $N=2$ temperature dependence of spin susceptibility (times the temperature) for several values of Hubbard $U$ as well as the data extracted for the Kondo lattice model.

Figure 7

Density of $f$-electron states obtained from the solution of the periodic Anderson model for the values of Hubbard $U=3,5,10$.

Figure 8

Conduction electron density of states obtained from the solution of the periodic Anderson model for the values of Hubbard $U=3,5,10$. Also shown is the result of the simulation with the Kondo lattice.

Figure 9

Conduction electron self-energy of the periodic Anderson model with $N=4$ calculated for several values of $U$ and the conduction electron self-energy of the Kondo lattice model that corresponds to $U\to \infty$ limit.

Figure 10

The convergence for the $f$-electron self-energy obtained from the periodic Anderson model with $N=4$ upon increase in the interaction $U$. The limiting behavior of this quantity extracted from the solution of the Kondo lattice model is also plotted.

Figure 11

Comparison between quasiparticle residues $z_f$ calculated as a function of Hubbard $U$ using periodic Anderson model with $N=4$, and the values extracted from the Kondo lattice model using two different approaches described in text.

Figure 12

Conduction electron self-energies $\mathfrak{R}{\Sigma }_c\left(\epsilon \right)$(top plot) and $\Im {\Sigma }_c\left(\epsilon \right)$ (bottom plot) of ${\Gamma }_7$ states for CeRhIn${}_5$ at temperature $T=0.002$ eV($\approx$23 K$)$ calculated using the LDA+DMFT method with the Kondo lattice.