  The spin$-1/2$ Heisenberg antiferromagnet on the honeycomb bilayer lattice is
shown to display a rich variety of semiclassical and genuinely quantum phases,
controlled by the interplay between intralayer frustration and interlayer
exchange. Employing a complementary set of techniques, comprising spin
rotationally invariant Schwinger boson mean field theory, bond operators, and
series expansions we unveil the quantum phase diagram, analyzing low-energy
excitations and order parameters. By virtue of Schwinger bosons we scan the
complete range of exchange parameters, covering both long range ordered as well
as quantum disordered ground states and reveal the existence of an extended,
frustration induced lattice nematic phase in a range of intermediate exchange
unexplored so far.
