Mott transition and ferrimagnetism in the Hubbard model on the anisotropic kagome lattice

Mott transition and ferrimagnetism are studied in the Hubbard model on the anisotropic kagome lattice using the variational cluster approximation and the phase diagram at zero temperature and half filling is analyzed. The ferrimagnetic phase rapidly grows as the geometric frustration is relaxed, and the Mott-insulator phase disappears in the moderately frustrated region showing that the ferrimagnetic fluctuations stemming from the relaxation of the geometric frustration are enhanced by the electron correlations. In the metallic phase, heavy-fermion behavior is observed and the mass-enhancement factor is computed. The enhancement of effective spatial anisotropy by the electron correlations is also confirmed in the moderately frustrated region and its effect on heavy-fermion behavior is examined.

Figure 1

(a) Anisotropic kagome lattice. In our lattice geometry, the three sites: $1$, $2$, and $3,$ form an equilateral triangle of the unit length and the dashed lines are along the $x$ direction. Inside the hexagon (dotted line) and square (dash-dotted line) are the 12- and 6-site clusters, respectively, which will be used in our analysis. (b) The first Brillouin zone of the anisotropic kagome lattice.

Figure 2

Phase diagram of the Hubbard model on the anisotropic kagome lattice at zero temperature and half filling as a function of $t^{\text{'}}$ and $U$ obtained by VCA, where the 12-site cluster is used (the crosses and circles). Solid lines are guides to the eye. The triangles and squares are the results obtained using the 6-site cluster. The crosses and triangles correspond to the ferrimagnetic and paramagnetic transition points and circles and squares are for the Mott transition points.

Figure 3

The double occupancy, $D_{\mathrm{occ}}$, as a function of $U$ for $t^{\text{'}}=1.0$, $0.8$, and $0.6$. The 12-site cluster is used. The three arrows indicate the Mott transition points.

Figure 4

Mott gap, $\Delta$, as a function of $U$ at (a) $t^{\text{'}}=1.0$, (b) $t^{\text{'}}=0.8$, and (c) and (d) $t^{\text{'}}=0.6$. These parameter regions correspond to the three vertical lines in Fig. 2. For $t^{\text{'}}=0.6$, the order parameter, $M$, is also included and the vertical lines separate the ferrimagnetic and MI phases.

Figure 5

(a) Spectral density at $t^{\text{'}}=0.75$, (b) $U=8$ (ferrimagnetic state), (c) $U=6$ (MI state), and (d) $U=3$ (metallic state) along the dotted line in Fig. 1b. The Lorentzian broadening with $\eta =0.15t$ is used in all cases. In (a) and (b), the solid lines are the mean-field SDW dispersion for the same values of $U$, $t^{\text{'}}$, and $\mu$. In (d), the solid lines are the noninteracting band structure. In (a), (b), and (c) the peaks are scaled by five times compared to (d).

Figure 6

(a) Ratio, $r$, as a function of $U$ for $t^{\text{'}}=1.0$, $0.8$, and $0.6$. The two arrows indicate the value of $r$ for a noninteracting band at $t^{\text{'}}=0.5$ ($r=1.24$) and at $t^{\text{'}}=0.4$ ($r=1.30$). (b)–(d) Mass enhancement factor, $m^{*}/m$, in the $x$ and $y$ directions as a function of $U$ for (b) $t^{\text{'}}=1.0$, (c) $t^{\text{'}}=0.8$, and (d) $t^{\text{'}}=0.6$. The solid lines are obtained using the 12-site cluster and the symbols (squares, triangles, and circles) are the results for the 6-site cluster. In (a), the squares, triangles, and circles correspond to $t^{\text{'}}=1.0$, $0.8$, and $0.6$, respectively. In (b)–(d), the triangles correspond to the $x$ direction while the squares correspond to the $y$ direction.