Density-wave and antiferromagnetic states of fermionic atoms in optical lattices

We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction.

Figure 1

(Color online) (a) Quasiparticle weight $Z$ and superfluid order parameter $\Phi$ as functions of $U$ $(<0)$ for $D=0$. (b) ADW order parameter $M_{\mathrm{ADW}}$ and $Z$ as functions of $U$ $(<0)$ for $D=0$. Inset: Atomic number per site of the $B$ $\left(A\right)$ sublattice $n_{B\left(A\right)}={\sum }_{\alpha ,\sigma }⟨n_{B\left(A\right)\alpha \sigma }⟩$.

Figure 2

(Color online) Energies of three states as functions of (a) $U$ $(<0)$ for $D=0$ and (b) $D$ for $U=-2.5$. MI indicates the Mott insulator.

Figure 3

(Color online) Single-particle excitation spectra ${\rho }_{A1}\left(\omega \right)$ for several values of $D$ at $U=-2.5$.

Figure 4

(Color online) (a) Quasiparticle weight $Z$ as a function of $U$ $(>0)$ for $D=0$. (b) ADW order parameter $M_{\mathrm{ADW}}$ and $Z$ at $D=0$. Inset: Atomic number per site of the $A$ sublattice with $\sigma$ $\left(\overline{\sigma }\right)$ pseudospin, $n_{A\sigma \left(\overline{\sigma }\right)}={\sum }_{\alpha }⟨n_{A\alpha \sigma \left(\overline{\sigma }\right)}⟩$.

Figure 5

(Color online) Energies of three states as functions of (a) $U$ $(>0)$ for $D=0$ and (b) $D$ for $U=2.0$. MI indicates the Mott insulator.

Figure 6

(Color online) Phase diagram for the two-band Hubbard model at half filling. The spheres with blue (dark) color represent atoms with “up” pseudospin and the spheres with red (light) color represent atoms with “down” pseudospin.

Figure 7

(Color online) (a) ADW order parameter $M_{\mathrm{ADW}}$ and superfluid order parameter $\Phi$ as functions of the attractive interaction $U$ for several values of $J$ in $U^{\prime }=U∕2$ and $D=0$. For $J=2U^{\prime }$, $M_{\mathrm{ADW}}∕2$ and $\Phi$ show the same $U$ dependence. (b) Energies of the ADW, superfluid, and Mott-insulating states are compared for several values of $J$ in $U^{\prime }=U∕2$ and $D=0$. At the arrows, the superfluid (SF) states change into Mott-insulating (MI) states. For $J=2U^{\prime }$, the energies of the superfluid and ADW states are degenerate.