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A number of topological nodes including Dirac, quadratic and triple bandtouching points as well as a pair of degenerate Dirac line nodes are found toemerge in the triplet plaquette excitations of the frustrated spin-1/2$J_1$-$J_2$ antiferromagnetic Heisenberg honeycomb model when the ground stateof the system lies in a spin-disordered plaquette-valence-bond-solid phase. Asix-spin plaquette operator theory of this honeycomb model has been developedfor this purpose by using the eigenstates of an isolated Heisenberg hexagonalplaquette. Spin-1/2 operators are thus expressed in the Fock space spanned bythe plaquette operators those are obtained in terms of exact analytic form ofeigenstates for a single frustrated Heisenberg hexagon. Ultimately, aneffective interacting boson model of this system is obtained on the basis oflow energy singlets and triplets plaquette operators by employing a mean-fieldapproximation. The values of ground state energy and spin gap of this systemhave been estimated and the validity of this formalism has been tested uponcomparison with the known results. Emergence of topological point and linenodes on the basis of spin-disordered ground state noted in this investigationis very rare on any frustrated system as well as the presence of triplet flatband. Evolution of those topological nodes is studied throughout the fullfrustrated regime. Finally, emergence of topological phases has been reportedupon adding a time-reversal-symmetry breaking term to the Hamiltonian.Coexistence of spin gap with either topological nodes or phases turns thishoneycomb model an interesting one.

Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice