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

Abstract: In the past decades, tremendous efforts have been made towards 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 unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small value of $N$, namely $N=2,3$, the ground state is antiferromagnetic (AFM) phase, whereas in the large-$N$ limit, valence bound solid (VBS) order is dominant. For the intermediate value of $N$ such as $N=4$, remarkably, our study reveals 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 spontaneously 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, but also offers a novel route towards searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.