  A number of topological nodes including Dirac, quadratic and triple band
touching points as well as a pair of degenerate Dirac line nodes are found to
emerge in the triplet plaquette excitations of the frustrated spin-1/2
$J_1$-$J_2$ antiferromagnetic Heisenberg honeycomb model when the ground state
of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A
six-spin plaquette operator theory of this honeycomb model has been developed
for this purpose by using the eigenstates of an isolated Heisenberg hexagonal
plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by
the plaquette operators those are obtained in terms of exact analytic form of
eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an
effective interacting boson model of this system is obtained on the basis of
low energy singlets and triplets plaquette operators by employing a mean-field
approximation. The values of ground state energy and spin gap of this system
have been estimated and the validity of this formalism has been tested upon
comparison with the known results. Emergence of topological point and line
nodes on the basis of spin-disordered ground state noted in this investigation
is very rare on any frustrated system as well as the presence of triplet flat
band. Evolution of those topological nodes is studied throughout the full
frustrated regime. Finally, emergence of topological phases has been reported
upon adding a time-reversal-symmetry breaking term to the Hamiltonian.
Coexistence of spin gap with either topological nodes or phases turns this
honeycomb model an interesting one.
