Determine the full pyrochlore quantum ground-state kernel

Determine a closed-form basis for the full quantum common kernel of the chiral color-ice parent Hamiltonian on the pyrochlore lattice, thereby enabling controlled degenerate perturbation theory over the entire zero-energy kernel.

Background

For corner-sharing checkerboard and pyrochlore lattices, the paper characterizes the coherent-product sector through Möbius coordinates and constructs a polarized subset through a matching representation. However, the complete many-body kernel also contains entangled zero-energy states. The absence of a closed-form description prevents systematic degenerate perturbation theory across the entire kernel, making the structure of the pyrochlore ground-state space an explicitly unresolved problem.

References

On the corner-sharing lattices we know the product-state sector of the kernel completely---the M"obius coordinates parametrize it---and we know the polarized matching states, but we do not have a closed-form basis for the full kernel of the pyrochlore model; controlled degenerate perturbation theory over the entire kernel is therefore still out of reach in general.

— Chiral Color Ice: Exact Local Handedness Constraints and Möbius Zero Modes in Frustrated Magnets  (2608.30802 - Kránitz et al., 31 Aug 2026) in Section 6, Outlook (Sec. 6 discussion of the corner-sharing lattices)

Whether that happens, or the ferromagnet wins, or an intermediate regime intervenes, is open on both the classical and the quantum side.

— Chiral Color Ice: Exact Local Handedness Constraints and Möbius Zero Modes in Frustrated Magnets  (2608.30802 - Kránitz et al., 31 Aug 2026) in Section 6, Outlook; related statement also appears in Section 1