Non-Fermi-Liquid Behavior in the Periodic Anderson Model

We study the Mott metal-insulator transition in the periodic Anderson model with dynamical mean field theory (DMFT). Near the quantum transition, we find a non-Fermi-liquid metallic state down to a vanishing temperature scale. We identify the origin of the non-Fermi-liquid behavior as being due to magnetic scattering of the doped carriers by the localized moments. The non-Fermi-liquid state can be tuned by either doping or external magnetic field. Our results show that the coupling to spatial magnetic fluctuations (absent in DMFT) is not a prerequisite to realizing a non-Fermi-liquid scenario for heavy fermion systems.

Figure 1

Density of states for $p$ and $d$ electrons (solid and dashed line, respectively) from QMC data at $T=1/128$. The doping is $\delta =0.049$, $\mu =0.53$, $\Delta =1$, $U=2$, and $t_{pd}=0.9$. The analytic continuation is done using the maximum entropy method. Inset: DOS of $p$ and $d$ electrons in the Mott-Hubbard insulating phase. The chemical potential is $\mu =1.08$ and the occupation is $n=n_d+n_p=3$, with $n_d=1+\nu$, $n_p=2-\nu$, and $\nu =0.14$. ${\Delta }_M$ denotes the Mott insulating gap.

Figure 2

Imaginary parts of the $p$-electron self-energy $\mathrm{Im}{\Sigma }_{pp}(i{\omega }_n)$ in the NFL state, from QMC calculations at $T=1/128$. The hole doping is $\delta =0.016$ (squares), $\delta =0.049$ (circles), $\delta =0.093$ (triangles), and $\mu =0.58$, 0.53, and 0.48, respectively. Solid line is the same quantity from ED-DMRG. The ED-DMRG data are obtained for large finite clusters of 40 sites and are plotted down to the frequency of the lowest energy pole. Inset: inverse scattering time $\mathrm{Im}{\Sigma }_{pp}(\omega \to 0)$ as a function of temperature. The black symbols are for the same values of $\delta$ as in the main panel. Open symbols are for higher doping $\delta =0.44$ (circles) and 0.62 (squares) with $\mu =0.23$ and 0.13, respectively. Note that the inverse scattering time goes to 0 in the Fermi liquid state.

Figure 3

Intensity plot of the scattering rate $\mathrm{Im}{\Sigma }_{pp}(\omega \to 0)$ as a function of doping $\delta$ and $T$. For visualization, the scattering rates are normalized to $\max \{\mathrm{Im}{\Sigma }_{pp}({\omega }_n)\}$ at each ($\delta$, $T$). The line with squares at low $\delta$ is $T_{\mathrm{Neel}}$ and gives the AFM phase boundary. (The $T=0$ data point is obtained from ED.) The line with circle dots denotes the numerical estimate for the crossover scale $T_{\mathrm{coh}}$. It is obtained from the extrapolation of the low $T$ behavior of $1/{\chi }_{\mathrm{loc}}(T)$ (see text).

Figure 4

Intensity plot of the scattering rate $\mathrm{Im}{\Sigma }_{pp}(\omega \to 0)$ as a function of external magnetic field $B$ and $T$, at fixed doping $\delta =0.01$. For visualization, the scattering rates are normalized to $\max \{\mathrm{Im}{\Sigma }_{pp}({\omega }_n)\}$ at each ($B$, $T$).