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Kitaev Honeycomb Spin Liquid

Interactive 3D Kitaev honeycomb model: tune the three bond couplings Jx/Jy/Jz to cross the real gapped-to-gapless quantum spin liquid phase boundary, watch the live Majorana dispersion surface over the Brillouin zone, and click bonds to inject Z2 flux defects.

Quantum Physics3DAdvanced60 FPS📱 Mobile-adapted

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 honeycomb lattice with its three bond-dependent couplings (Jx, Jy, Jz) and, above it, a live 3D surface of the exact Majorana dispersion |f(k)| over the Brillouin zone — drag the sliders and watch the surface's 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.

⚙ Under the hood

Tune the three bond couplings of the exactly-solvable Kitaev honeycomb model and watch the real Majorana dispersion surface cross the gapped-to-gapless quantum spin liquid phase boundary; click any bond to inject a real Z2 flux-vortex defect.

quantum spin liquidKitaev modelMajorana fermionstopological ordercondensed matterhoneycomb lattice

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install