Extended Data Figure 6: Calculation of the π-flux Hamiltonian.

a, Flux pattern and real nearest-neighbour hoppings on the triangular lattice. In the figure, ‘+t’ denotes t_ij = t_ji = t and ‘−t’ denotes t_ij = t_ji = −t; ‘π’ denotes triangles that are threaded by a π flux. b, Spinon band structure of the π-flux Hamiltonian. The two bands are particle–hole related, both with bandwidths of 3t. c, Calculated momentum dependence of the dynamic spin structure factor at low energy ω = 2.1t. Strong peaks can be distinguished at the Γ point, the point ((1/2, −1/2) in r.l.u.) and equivalent positions. White dashed lines denote the zone boundaries. d, Calculated dynamic spin structure factor along high-symmetry points with η = 0.3t.