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We extend Quantum Dimer Model (QDM) introduced by Rokhsar and Kivelson insuch a way that the model includes resonance processes on larger loops. Thestrategy is to first construct a pseudo spin Hamiltonian which is defined notby the S =1/2 but by the S=1 representation and then establish thecorrespondence between the pseudo-spin-1 configurations and those of dimers.The standard QDM keeps only the lowest resonance processes for pairs ofparallel dimers and its validity in describing the realistic spin systems isnot obvious. Our extended QDM (EQDM) improves this point and contains a novelresonance term, which is equivalent to two successive actions of the familiarparallel dimer resonance. For a certain choice of the coupling constants, ourmodel exhibits three exotic valence-bond phases (herringbone, checkerboard and'dimer smectic') in the ground state, which meet at a triple point. Thecheckerboard phase has four-fold rotational symmetry, while the dimer smecticis characterized by partial ordering only in one of the two directions. In thedimer smectic phase, we investigate the dimer-dimer correlation by using ananalogy to random walks.

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