2007/05/31 by Sergey Pankov, S. Pankov, Roderich Moessner +2 · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.76.104436
published as Phys. Rev. B 76, 104436 (2007) · 12 pages, 15 figures, minor changes, references added, Phys Rev B version
openalex publication_date 2007/09/27 · arxiv created 2008/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 [Phys. Rev. Lett. 61, 2376 (1988)] 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.