Dynamical mean-field theory for flat-band ferromagnetism

The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.

Figure 1

The ideal structure of perovskite compounds ${\mathrm{ABX}}_3$. The corner-sharing octahedra ${\mathrm{BX}}_6$ form an edge-centered cubic lattice.

Figure 2

The filling $n_c$ of $c$ electrons as a function of the energy level ${\varepsilon }_c$ at $U=5$ and $\mu =U/2$ $\left(t^{*}=1\right)$.

Figure 3

The magnetization $m_c$ via the filling $n_c$ of $c$ electrons for different values of the chemical potential $\mu$. PS denotes the phase separation region. $U=5,t^{*}=1$.

Figure 4

The magnetization $m_c$ of the hypercube $C$ as a function of the Coulomb interaction $U$ at half filling $\mu =U/2$ and ${\varepsilon }_c=0$. $t^{*}=1$.

Figure 5

Magnetic phase diagram of the hypercube $C$. SF (UF) denotes the fully saturated (unsaturated) ferromagnetism. The phase separation occurs on the phase boundaries. $U=5,t^{*}=1$.

Figure 6

The density of states (DOS) of electrons of the $C$ and $A$ sublattices at half filling $\left(\mu =U/2,{\varepsilon }_c=0\right)$ in the two-dimensional Lieb lattice. The blue solid lines, the green dotted lines, and the red filled circles are the DOS calculated by the DMFT with the modified ED $\left(n_s^c=n_s^a=3\right)$, the standard ED $\left(n_s^c=n_s^a=5\right)$, and the NRG, respectively. The NRG results are reproduced from Ref. [15].

Figure 7

The interaction dependence of the sublattice magnetizations calculated by the DMFT with NRG, the modified ED (MED) $\left(n_s^c=n_s^a=3\right)$, and the standard ED (SED) $\left(n_s^c=n_s^a=5\right)$ at half filling $\left(\mu =U/2,{\varepsilon }_c=0\right)$ in the two-dimensional Lieb lattice. The NRG results are reproduced from Ref. [15].

Figure 8

The temperature dependence of the sublattice magnetizations calculated by the DMFT with the modified ED $\left(n_s^c=n_s^a=3\right)$ at half filling $\left(\mu =U/2,{\varepsilon }_c=0\right)$ in the two-dimensional Lieb lattice.