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 SU($N$) symmetry and the frustration in a $J_1$-$J_2$ 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.