Single-particle excitation-spectra in the Hubbard model on a kagom\'{e} lattice

The effects of frustration in spin systems have been studied for many years. Recently, the transport properties of the layered cobalt oxide Na$_{x}$CoO$_{2}$ and of related oxides have generated new interest in the frustrated systems. In the cobalt oxides, the Co ions form a triangular lattice. The hopping matrix element of electrons in the cobalt 3$d$ orbitals is not isotropic, and we have shown [PRL\textbf{91}, 257003] that the triangular CoO$_{2}$ lattice consists of four coupled kagom\'{e} sublattices. For this reason, here, we examine the single-particle excitation spectrum of the Hubbard model on the kagom\'{e} lattice, and study the motion of a carrier in this frustrated system. We use the quantum Monte Carlo and the exact-diagonalization methods. The dispersion relation of the tight-binding model on the kagom\'e lattice has a flat dispersion at the top or the bottom of the energy band depending on the sign of hopping-matrix element $t$. This causes a two-fold degeneracy at the $\Gamma$ point where the flat piece of the dispersion is located. However, in the interacting system, we find that the lowest- lying states have a two-fold degeneracy at the $\Gamma$ point independent of the sign of $t$, when the Coulomb repulsion is sufficiently strong. In this talk, we will discuss these numerical results on the electronic structure of the Hubbard model on the kagom\'{e} lattice.