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

TL;DR

This paper explores the orbital exchange interactions in $p$-band Mott-insulators on various lattices, revealing frustration effects and quantum fluctuation-driven ordering patterns, with implications for optical lattice systems.

Contribution

It introduces a novel quantum 120°-model for orbital exchange on the honeycomb lattice and analyzes quantum fluctuation effects leading to specific orbital orderings.

Findings

Orbital orders are found in triangular and Kagome lattices.

Orbital exchange on the honeycomb lattice is frustrated, described by a new quantum 120°-model.

Quantum fluctuations induce a six-site plaquette orbital order via order-from-disorder.

Abstract

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. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the ``order from disorder'' mechanism. This effect arises from the appearance of a zero energy flat-band of orbital excitations.