  The recent observation of magnetization plateaus in rare-earth metallic
tetraborides has drawn a lot of attention to this class of materials. In this
work, we investigate the electronic structure of one such canonical system
$\textrm{LuB}_{4}$, using first-principle density functional theory, together
with strong Coulomb correlation and spin-orbit coupling (SOC) effects. The
electronic band structures show that $\textrm{LuB}_{4}$ is a non-magnetic
correlated metal with completely filled $4f$ shell. The projected density of
states (DOS) shows a continuum at the Fermi level (FL), arising mainly from
hybridized Lu $d$ and B $p$ orbitals, along with some discrete peaks, well
separated from the continuum. These peaks arise mainly due to core-level Lu
$s$, $p$ and $4f$ atomic orbitals. Upon inclusion of SOC, the discrete peak
arising due to Lu $p$ is split into two peaks with $j = 1/2$, $j = 3/2$ while
the peak arising due to Lu $4f$ orbitals splits into two peaks with $j = 5/2$
and $j = 7/2$. These peaks will give rise to multiplet structure in core level
X-ray photo-emission spectroscopy. Inclusion of strong correlation effects
pushes the Lu $4f$ peak away from the FL while the qualitative features remain
intact.
