Fig. 4: Nonequilibrium response of the spinon density to a temperature cycle.

a Schematic illustration of the nonequilibrium spinon density. The system is initially prepared in equilibrium at temperature T_b. If temperature is then lowered at a sufficiently large rate, ρ_s falls out of equilibrium—the patches grow in diameter but their diffusive motion is slow. At T_c, the typical separation of the patches becomes comparable to their radius ξ, and the closest pairs begin to annihilate. The density then remains kinematically locked to 1/ξ² as pairs continue to annihilate. If the direction of temperature variation is then reversed at T_d, ρ_s develops another plateau as pairwise annihilation of spinons ceases and the diameter of the patches shrinks. This continues until a sufficiently high temperature, T_e, is reached at which thermodynamic equilibrium is restored. The behaviour of the vison-depleted patches at each of these temperatures is depicted in b–e. The patches are qualitatively represented by the solid circles and identified by the colour of their Voronoi cell.