Kondo effect in Lieb's minimal ferrimagnetic system on the T-shaped bipartite lattice

The minimal ferrimagnetism by Lieb's theorem emerges on the T-shaped bipartite lattice composed of four sites, which can be realized experimentally, just as Nagaoka ferromagnetism has been demonstrated experimentally using a quartet quantum dot [J. P. Dehollain et al., Nature (London) 579, 528 (2020)]. In this paper, the Kondo effect on this ferrimagnetism is theoretically studied. The magnetic moment $S=1$ is screened in two steps by the Kondo effect and the series conductance $g_s$ is strongly suppressed to $g_s\simeq 0$, while the parallel conductance $g_p$ has the maximum value $g_p\simeq 4e^2/h$. The robustness of these properties against a parameter change toward reducing the Lieb's ferrimagnetism is also discussed, showing the scenarios for entanglement of the degrees of freedom toward the ground state.

Figure 1

Schematic picture of (a) series and (b) parallel configurations.

Figure 2

(a) The spin quantum number and the electron occupation number of the ground state of the isolated Hubbard model on the T-shaped lattice as functions of $(2{\varepsilon }_d+U)/t$ and $U/t$. (b) The probabilities $P_S$ and $P_D$ plotted as functions of $U/t$. Examples of $S$ and $D$ states are presented in this figure.

Figure 3

The spin correlations between two sites in sublattice $A$ (blue circle) and between site $i$ in sublattice $A$ and site $j(=2)$ in sublattice $B$ (red inverted triangle) plotted as functions of $U/t$.

Figure 4

Two kinds of conductance $g_s,g_p$ and the phase shifts ${\delta }_e,{\delta }_o$ obtained using our method are compared with the exact results for $U=0$. Here $\mathrm{\Gamma }/t=0.1$. For NRG, we use $\mathrm{\Lambda }=6$ and $t/D=0.1$.

Figure 5

Temperature dependencies of the impurity entropy for several values of $U$ calculated using NRG energy spectrum. Inset: The $U_3/U$ dependencies of the impurity entropy.

Figure 6

$\mathrm{\Gamma }$ dependence of the impurity entropy for $U/t=4$.

Figure 7

Two kinds of conductance $g_s,g_p$, the electron occupation number $n$ in the T-shaped lattice, and the phase shifts ${\delta }_e$ and ${\delta }_o$ plotted as functions of ${\varepsilon }_d/t$ for $U/t=4$.

Figure 8

Two kinds of conductance $g_s$ and $g_p$ plotted as functions of $t_3/t$ with discontinuities at $t_3/t=0$. Inset: Temperature dependencies of the impurity entropy for $t_3/t=0.01$ and 0.1 compared with the result for $t_3/t=1$.