Intertwining SU( N ) symmetry and frustration on a honeycomb lattice

Large symmetry groups in quantum many-body systems could strongly enhance quantum fluctuations and thereby stabilize exotic quantum phases. Frustrated interactions were long known to have similar effects. Here we intertwine the large $\mathrm{SU}(N$) symmetry and the frustration in a ${J}₁\text{\ensuremath{-}}{J}₂\phantom{\rule{0.16em}{0ex}}\mathrm{SU}(N$) Heisenberg model on a honeycomb lattice, where ${J}₁$ is the nearest-neighbor coupling and ${J}₂$ is the next-nearest-neighbor coupling. With a large-$N$ analysis, we obtain a rich phase diagram by varying both $N$ and the ratio ${J}₂/{J}₁$. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.