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

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.

References in corpus (12)

• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations
• Exotic many-body physics with large-spin Fermi gases
• Spin nematic ground state of the triangular lattice S=1 biquadratic model
• Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain
• The Néel-VBS transition in three-dimensional SU($N$) antiferromagnets

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