Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions

In the past few decades, tremendous efforts have been made toward understanding the exotic physics emerging from competition between various ordering tendencies in strongly correlated systems. Employing state-of-the-art quantum Monte Carlo simulation, we investigate an interacting SU(N) fermionic model with varying interaction strength and value of N, and we unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small values of N-namely, N=2, 3-the ground state is an antiferromagnetic (AFM) phase, whereas in the large-N limit, a staggered valence bond solid (VBS) order is dominant. For intermediate values of N such as N=4, 5, remarkably, our study reveals that distinct VBS orders appear in the weak and strong coupling regimes. More fantastically, the competition between staggered and columnar VBS ordering tendencies gives rise to a Mott insulating phase without spontaneous symmetry breaking (SSB), existing in a large interacting parameter regime, which is consistent with a gapped quantum spin liquid. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems-it also offers a novel route toward searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.