Showing papers by "Shivaji Lal Sondhi published in 2007"
TL;DR: In this paper, the authors considered the simplest generalizations of the valence bond physics of SU(2) singlets to SU(3) and SU(4) singlet plaquettes in three dimensions and showed that the ground state is solid everywhere, including at the Rokhsar-Kivelson point where the ground states are an equal amplitude sum.
Abstract: We consider the simplest generalizations of the valence bond physics of SU(2) singlets to $\mathrm{SU}(N)$ singlets that comprise objects with $N$ sites---these are $\mathrm{SU}(N)$ 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.
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