We show how to construct fully symmetric states without topological order on a honeycomb lattice for $S=\frac{1}{2}$ spins using the language of projected entangled pair states. An explicit example is given for the virtual bond dimension $D=4$. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking in the proposed wave functions are checked by numerical calculations of the entanglement entropy and various correlation functions. Exponential decay of all correlation functions measured are strongly indicative of the energy gap for the putative parent Hamiltonian of the state. Our work provides the first explicit realization of a featureless quantum state for spin-$\frac{1}{2}$ particles on a honeycomb lattice.

• Received 14 September 2015
• Revised 12 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.064432