Metal-Insulator Transitions in the Periodic Anderson Model

We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime.

Figure 1

Density of states for the $p$ and $d$ electrons (dashed and solid line) for $\Delta =1$, $t_{\mathrm{pd}}=0.9$. Upper panel shows the $U=0$ case with $\mu =0.529$ that gives a total occupation of three particles below the Fermi energy. The lower panel shows analytically continued QMC data for the Mott insulator state with $U=2$, $T=1/64$, and $\mu =1.079$ that gives $n_{\mathrm{tot}}=3$. The double arrow head line indicates the large Mott gap ${\Delta }_M$. The inset shows ${\Delta }_M(U)$ for different positions of the of the $p$-electron band ${ϵ}_p=-6$, $-3$, $-2$, $-1$ (top to bottom). The results are obtained with ED of finite clusters of $N_s$ sites and the data shown are for the limit $N_s\to \infty$.

Figure 2

$n_d$ (solid line), $n_p$ (dashed line), and $n_{\mathrm{tot}}$ (dotted line) as a function of $\mu$, for $U=2$. The data are from QMC at $\Delta =1$, $t_{\mathrm{pd}}=0.9$, and $T=1/64$. The plateaux at $n_{\mathrm{tot}}=2$ and 4 are band insulator (BI) states. The one at $n_{\mathrm{tot}}=3$ is the Mott insulator (MI). The inset shows the phase diagram in the $U\mathrm{\text{−}}\mu$ plane. The boundary lines are for $T=1/20$ (dotted line), $T=1/64$ (thick solid line), and $T=0$ (thin solid line). The dashed thick line segment at $T=1/64$ denotes the region of the MIT boundary where the QMC data show coexistence of a metal and an insulating solution. The $T=0$ data are from extrapolated ED calculations. This method is not suited for the study of coexistence of solutions at $T=0$. The dash-dotted line denotes the transition from a metal ($M$) to the band insulator (BI) at $n_{\mathrm{tot}}=4$.

Figure 3

Density of states of $p$ and $d$ electrons (dashed and solid line) for $U=2$, $\Delta =1$, $t_{\mathrm{pd}}=0.9$, and $T=1/64$, as obtained from QMC. Upper panel: $\mu =0.554$, which corresponds to tiny hole doping. Lower panel: $\mu =1.234$, which corresponds to tiny particle doping.

Figure 4

$⟨m_d^z{m}_p^z⟩$ as a function of $\mu$, for $U=2$, $\Delta =1$, $t_{\mathrm{pd}}=0.9$. The results are obtained from ED with a cluster of 16 sites.