Orbital ordering and frustration of $p$-band Mott-insulators

Understand

We investigate the general structure of orbital exchange physics in Mott-insulating states of $p$-orbital systems in optical lattices.

• Orbital orders occur in both the triangular and Kagome lattices.
• In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120$^\circ$-model.
• Its classical ground states are mapped into configurations of the fully-packed loop model with an extra U(1) rotation degree of freedom.