Energy scales of the doped Anderson lattice model

This paper explores the energy scales of the doped Anderson lattice model using dynamical mean-field theory (DMFT), using a continuous-time quantum Monte Carlo (CTQMC) impurity solver. We show that the low temperature properties of the lattice cannot be scaled using the single ion local Kondo temperature $T_K$ but instead are governed by a doping-dependent coherence temperature $T^{*}$ which can be used to scale the temperature dependence of the spectral function, transport properties, and entropy. At half-filling $T^{*}$ closely approximates the single ion $T_K$, but as the filling $n_c$ is reduced to zero, $T^{*}$ also vanishes. The coherence temperature $T^{*}$ is shown to play a role of effective impurity Kondo temperature in the lattice model, and physical observables show significant evolution at $T^{*}$. In the DMFT framework we showed that the hybridization strength of the effective impurity model is qualitatively affected by the doping level, and determines $T^{*}$ in the lattice model.

Figure 1

Local static spin susceptibility of the Anderson lattice model scaled (a) by $T_K$ and (b) by $T^{*}$, computed at chemical potential $\mu =-0.8$, for a range of hybridization between $V=0.18$ (red) and $V=0.54$ (purple). The dashed lines are the best fit and the error bars show the mismatch between the best-fit line and actual data. (c) Schematic phase diagram showing the variation of $T^{*}$ with chemical potential, and the regions where the data scales with $T_K$ (red) and with $T^{*}$ (blue). The dashed line is a guide to the eye.

Figure 2

Intensity plots showing the momentum and energy resolved conduction electron spectral function (a) as a function of momentum and (b) at fixed $E=0$, showing the evolution of the Fermi surface with temperature, for $\mu =-0.5$.

Figure 3

Area of the Fermi surface (a) and (b) and imaginary part of the $T$ matrix of the conduction electrons at the Fermi level (c) and (d) scaled by $T_K$ and $T^{*}$.

Figure 4

Resistivity (a) and (b) and entropy (c) and (d) scaled by $T_K$ and $T^{*}$.

Figure 5

Ratio between effective hybridization strength of the lattice model (${\mathrm{\Delta }}_0^{\text{latt}}$) and hybridization strength of the impurity model.