Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice

TL;DR

This paper introduces an SO(N) spin model on the triangular lattice, revealing diverse phases including spin nematics, valence-bond solids, and spin liquids, with a rich phase diagram featuring various phase transitions.

Contribution

It presents a sign-problem-free quantum Monte Carlo model for SO(N) spins on non-bipartite lattices, enabling detailed phase diagram exploration.

Findings

Evidence for spin nematic phase at small N

Observation of valence-bond solid at large N

Discovery of quantum spin liquid at intermediate N

Abstract

We introduce a simple model of SO($N$) spins with two-site interactions which is amenable to quantum Monte-Carlo studies without a sign problem on non-bipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small $N$, a valence-bond solid (VBS) at large $N$ and a quantum spin liquid at intermediate $N$. By the introduction of a sign-free four-site interaction we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions.