Kitaev Honeycomb Spin Liquid (2D)

The Kitaev honeycomb model is the rare strongly-interacting quantum magnet that can be solved exactly: each spin fractionalizes into an itinerant Majorana fermion moving through a static Z2 gauge field. This simulator renders a real, pannable honeycomb lattice with its three bond-dependent couplings (Jx, Jy, Jz) and, below it, a live heatmap of the exact Majorana dispersion |f(k)| over the Brillouin zone — drag the sliders and watch the heatmap's dark minimum rise off zero as you leave the gapless quantum-spin-liquid region and enter a gapped, topologically ordered phase. Clicking any bond performs the model's real elementary excitation move: flipping its Z2 gauge variable, which nucleates a pair of flux vortices on the two hexagons it borders.