SO($N$) singlet projection model on the kagome lattice

TL;DR

This study uses quantum Monte Carlo simulations to explore an SO(N) singlet projection model on the kagome lattice, revealing persistent spin-liquid phases at intermediate N and the absence of VBS phases at large N.

Contribution

It provides the first comprehensive quantum Monte Carlo analysis of an SO(N) model on the kagome lattice, highlighting differences from SU(N) models and identifying phase boundaries.

Findings

Spin-liquid phases exist for intermediate N.

No valence bond solid phase at large N.

Spin order persists up to N=8 and disappears at N=10.

Abstract

We present an extensive quantum Monte Carlo study of a nearest-neighbor, singlet-projection model on the kagome lattice that exhibits SO($N$) symmetry and is sign-problem-free. We find that in contrast to the previously studied SU($N$) variations of this model, the non-bipartite lattices appear to harbor spin-liquid phases for intermediate values of $N$, a result also seen on the triangular lattice with this same model. Unlike the triangular lattice, however, the kagome lattice appears to admit no valence bond solid (VBS) phase for large $N$, instead remaining a spin-liquid. We also observe that the spin-ordered phase survives to a relatively large value of $N$, at least $N=8$, and that it is gone for $N=10$; the fate of $N=9$ remains unclear.