Spin-induced orbital frustration in a hexagonal optical lattice

Complex lattices provide a versatile ground for fascinating quantum many-body physics. Here, we propose an exotic mechanics generating orbital frustration in hexagonal lattices. We study two-component (pseudospin-$1/2$) Bose gases $p$-orbital bands of two-dimensional lattices, and find that the system exhibits previously untouched as result interplay spin degrees freedom, contrast to normal Ising-type ordering spinless band bosons Based on classification by symmetry analysis, strong interaction leads Mott superfluid phases with spin-orbital intertwined orders, spite complete absence Hamiltonian. Our implies correlations multi-orbital setting could induce rich physics complex lattice structures.