Orbital ice: an exact Coulomb phase on the diamond lattice

TL;DR

This paper demonstrates the existence of an orbital Coulomb phase as the exact ground state in a p-orbital exchange model on the diamond lattice, revealing emergent gauge structures and orbital ice rules.

Contribution

It introduces an orbital ice model with emergent geometrical frustration and maps its ground states to spin-ice states, providing insights into quantum orbital dynamics.

Findings

Orbital ice exhibits algebraic dipolar correlations.

Emergent gauge structure from local orbital constraints.

Potential realization in cold atom optical lattices.

Abstract

We demonstrate the existence of orbital Coulomb phase as the exact ground state of p-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that the orbital ice model exhibits an emergent geometrical frustration by mapping the degenerate quantum orbital ground states to the spin-ice states obeying the 2-in-2-out constraints on the pyrochlore lattice. We also discuss possible realization of the orbital ice model in optical lattices with p-band fermionic cold atoms.