Resonating singlet valence plaquettes

TL;DR

This paper explores generalizations of valence bond physics to SU(N) singlets with N=3 and 4, analyzing their phases and discovering that SU(4) models tend to be solid, while SU(3) models can host liquid phases.

Contribution

It extends the Rokhsar-Kivelson quantum dimer model to SU(4) and SU(3) singlet plaquettes, analyzing their phase diagrams and identifying conditions for liquid versus solid phases.

Findings

SU(4) ground state is solid at the Rokhsar-Kivelson point.

SU(3) singlet triangular plaquettes can form a liquid phase.

The phase behavior depends on the lattice and the specific SU(N) model.

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 thus a candidate for describing a resonating single valence plaquette phase, given a suitably defined local Hamiltonian.