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Dimer Smectic in Extended Quantum Dimer Model -approach from pseudo S=1 Hamiltonian-

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.