  The spin-1/2 Heisenberg antiferromagnet on the distorted honeycomb (DHC)
lattice is studied by means of the tensor renormalization group method. It is
unveiled that the system has a quantum phase transition of second-order between
the gapped quantum dimer phase and a collinear Neel phase at the critical point
of coupling ratio \alpha_{c} = 0.54, where the quantum critical exponents \nu =
0.69(2) and \gamma = 1.363(8) are obtained. The quantum criticality is found to
fall into the O(3) universality class. A ground-state phase diagram in the
field-coupling ratio plane is proposed, where the phases such as the dimer,
semi-classical Neel, and polarized phases are identified. A link between the
present spin system to the boson Hubbard model on the DHC lattice is also
discussed.
