Nonzero angular momentum density wave phases in SU(N) fermions with singlet-bond and triplet-current interactions

We employ the sign-problem-free projector determinant quantum Monte Carlo method to study a microscopic model of SU(N) fermions with singlet-bond and triplet-current interactions on the square lattice. We find the gapped singlet p_x and gapless triplet d_x²-y² density wave states in the half-filled N=4 model. Specifically, the triplet d_x²-y² density wave order is observed in the weak triplet-current interaction regime. As the triplet-current interaction strength is further increased, our simulations demonstrate a transition to the singlet p_x density wave state, accompanied by a gapped mixed-ordered area where the two orders coexist. With increasing the singlet-bond interaction strength, the triplet d_x²-y²-wave order persists up to a critical point after which the singlet p_x density wave state is stabilized, while the ground state is disordered in between the two ordered phases. The analytical continuation is then performed to derive the single-particle spectrum. In the spectra of triplet d_x²-y² and singlet p_x density waves, the anisotropic Dirac cone and the parabolic shape around the Dirac point are observed, respectively. As for the mixed-ordered area, a single-particle gap opens and the velocities remain anisotropic at the Dirac point.