  Recently, a concept of orthogonal metal has been introduced to reinterpret
the disordered state of slave-spin representation in the Hubbard model as an
exotic gapped metallic state. We have extended this concept to study the
slave-spin representation of Hubbard model on the honeycomb lattice.[Phys. Rev.
B \textbf{86}, 165134 (2012)] It is found that a novel gapped metallic state
coined orthogonal Dirac semimetal is identified. Such state corresponds to the
disordered phase of slave-spin and has the same thermal-dynamical and transport
properties as Dirac semimetal but its singe-particle excitation is gapped. More
importantly, for generical orthogonal metallic states, the electron spectral
function which may be probed in future angle-resolved photoemission
spectroscopy (ARPES) experiments are studied.
