### Abstract

We consider the simplest generalizations of the valence bond physics of SU(2) singlets to SU (N) singlets that comprise objects with N sites-these are SU (N) singlet plaquettes with N=3 and N=4 in three spatial dimensions. Specifically, we search for a quantum mechanical liquid of such objects-a resonating singlet valence plaquette phase that generalizes the celebrated resonating valence bond phase for SU(2) spins. We extend the Rokhsar-Kivelson construction of the quantum dimer model to the simplest SU(4) model for valence plaquette dynamics on a cubic lattice. The phase diagram of the resulting quantum plaquette model is analyzed both analytically and numerically. We find that the ground state is solid everywhere, including at the Rokhsar-Kivelson point where the ground state is an equal amplitude sum. By contrast, the equal amplitude sum of SU(3) singlet triangular plaquettes on the face-centered cubic lattice is liquid and is thus a candidate for describing a resonating single valence plaquette phase, given a suitably defined local Hamiltonian.

Original language | English (US) |
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Article number | 104436 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 76 |

Issue number | 10 |

DOIs | |

State | Published - Sep 27 2007 |

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*76*(10), [104436]. https://doi.org/10.1103/PhysRevB.76.104436