  A novel gapped metallic state coined orthogonal Dirac semimetal is proposed
in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of
Hubbard model. This state corresponds to the disordered phase of slave-spin and
has the same thermaldynamical and transport properties as usual Dirac semimetal
but its singe-particle excitation is gapped and has nontrivial topological
order due to the $Z_{2}$ gauge structure. The quantum phase transition from
this orthogonal Dirac semimetal to usual Dirac semimetal is described by a
mean-field decoupling with complementary fluctuation analysis and its
criticality falls into the universality class of 2+1D Ising model while a large
anomalous dimension for the physical electron is found at quantum critical
point (QCP), which could be considered as a fingerprint of our fractionalized
theory when compared to other non-fractionalized approaches. As byproducts, a
path integral formalism for the $Z_{2}$ slave-spin representation of Hubbard
model is constructed and possible relations to other approaches and the
sublattice pairing states, which has been argued to be a promising candidate
for gapped spin liquid state found in the numerical simulation, are briefly
discussed. Additionally, when spin-orbit coupling is considered, the
instability of orthogonal Dirac semimetal to the fractionalized quantum spin
Hall insulator (fractionalized topological insulator) is also expected. We hope
the present work may be helpful for future studies in $Z_{2}$ slave-spin theory
and related non-Fermi liquid phases in honeycomb lattice.
