Tangle of Spin Double Helices in the Honeycomb Kitaev-$\mathrm{\Gamma }$ Model

We investigate the ground-state nature of the honeycomb Kitaev-$\mathrm{\Gamma }$ model in the material-relevant parameter regime through a combination of classical and quantum simulations. The classical model is imprinted with a tangle of highly structured spin double helices. This helix tangle exhibits $18$ inequivalent helical axes and features a spontaneous periodicity anisotropy and a $\mathrm{s}\mathrm{g}\mathrm{n}(\mathrm{\Gamma })$-determined chirality pattern. Infinite PEPS simulations with clusters up to $36$ sites identify hallmarks of this many-body order in the quantum spin-$1\mathrm{/}2$ model. Our findings provide a fresh perspective of the Kitaev-$\mathrm{\Gamma }$ model and enrich the physics of Kitaev magnetism.