  We extend Quantum Dimer Model (QDM) introduced by Rokhsar and Kivelson in
such a way that the model includes resonance processes on larger loops. The
strategy is to first construct a pseudo spin Hamiltonian which is defined not
by the S =1/2 but by the S=1 representation and then establish the
correspondence between the pseudo-spin-1 configurations and those of dimers.
The standard QDM keeps only the lowest resonance processes for pairs of
parallel dimers and its validity in describing the realistic spin systems is
not obvious. Our extended QDM (EQDM) improves this point and contains a novel
resonance term, which is equivalent to two successive actions of the familiar
parallel dimer resonance. For a certain choice of the coupling constants, our
model exhibits three exotic valence-bond phases (herringbone, checkerboard and
'dimer smectic') in the ground state, which meet at a triple point. The
checkerboard phase has four-fold rotational symmetry, while the dimer smectic
is characterized by partial ordering only in one of the two directions. In the
dimer smectic phase, we investigate the dimer-dimer correlation by using an
analogy to random walks.
