Destabilization of ferromagnetism by frustration and realization of a nonmagnetic Mott transition in the quarter-filled two-orbital Hubbard model

The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t^{\prime }$ in addition to the nearest-neighbor hopping $t$. For $t^{\prime }=0$, a ferromagnetic state with staggered orbital order occurs by increasing the Coulomb interaction $U$ before the Mott transition takes place. By increasing $t^{\prime }$, the region of this ferromagnetic phase shrinks, and the Mott transition without magnetic order occurs.

Figure 1

Correlation factors for the GWF and DHWF. Here, we show them for the single-orbital model for simplicity. When a pair of a doublon and a holon is created, the factor $g$ appears (middle panels). In the GWF, the doublon and holon move freely without a change in the factor (top right panel). In the DHWF, the factors ${\zeta }_0$ and ${\zeta }_{\uparrow \downarrow }$ appear when the pair separates (bottom right panel), where 0 and $\uparrow \downarrow$ denote the holon and doublon states, respectively. In this figure, we have considered only the nearest-neighbor doublon-holon binding factors for clarity.

Figure 2

Energy $E$ per site as a function of $U$ for the Jastrow wave function (Ref. [34], open symbols) and for the DHWF (solid symbols) for Hund's rule coupling $J=0$ (squares), $J=0.1U$ (circles), and $J=0.2U$ (triangles). The next-nearest-neighbor hopping $t^{\prime }$ is set to zero.

Figure 3

Energy $E$ per site as a function of $U$ in the PM (solid symbols) and FM (open symbols) states of the GWF (squares), of the Jastrow wave function (Ref. [34], triangles), and of the DHWF (circles) for $J=0.1U$. The next-nearest-neighbor hopping $t^{\prime }$ is set to zero.

Figure 4

Energy $E$ per site as a function of $U$ in the PM (solid symbols) and FM (open symbols) states for $L=10$ (squares), for $L=12$ (circles), and for $L=14$ (triangles) for $J=0.1U$. The next-nearest-neighbor hopping $t^{\prime }$ is set to zero.

Figure 5

Momentum distribution function $n\left(\mathit{k}\right)=\langle c_{\mathit{k}\tau \sigma }^{†}{c}_{\mathit{k}\tau \sigma }\rangle$ for $U=12t$, $J=0$, and $t^{\prime }=0$ in the PM phase. The renormalization factor $Z$ is estimated by extrapolating $n\left(\mathit{k}\right)$ from above and below the Fermi momentum along $(\pi ,\pi )$-(0,0) (dashed lines). Due to the antiperiodic boundary condition for the $x$ direction, we shift $k_x$ by $\pi /L$ ($L=12$); for example, $(\pi ,\pi )$ denoted in this figure actually means the point $(\pi -\pi /L,\pi )$.

Figure 6

Renormalization factor $Z$ as a function of $U$ for $J=0$ and $t^{\prime }=0$ in the PM phase for $L=10$ (squares), for $L=12$ (circles), and for $L=14$ (triangles). Here, we estimate $U_{\text{MIT}}$ by linearly extrapolating $Z$ to zero from data of $Z>0.1$ for $L=12$.

Figure 7

Phase diagrams for the two-orbital Hubbard model with the next-nearest-neighbor hopping $t^{\prime }$ (a) for $J=0$ and (b) for $J=0.05U$. The open circles with the dashed lines indicate the metal-insulator transition in the PM phase when we ignore the FM state.