Fig. 1

Spinons on decoupled chains. a An anisotropic AFM spin chain (top). If two spins are interchanged, two domain walls are created between the original antiferromagnetic domain (green) and a new domain (blue) (middle). Those domain walls form the basis for the propagating states carrying energy and momentum quanta (bottom). b The magnetic excitation spectrum and dispersion along the q_L direction in reciprocal space measured at T = 0.1 K, summed over −1 ≤ q_HH ≤ 1 rlu. The lower boundary of the spectrum (white circles) is shown along with the boundaries of the two spinon continuum obtained by fitting the lower boundary (red lines, Δ = 3.46) and comparing the total measured spectrum to theory (white lines, Δ = 2.6)²⁶. The color scale for parts b–d is shown above part c. Error bars represent one standard deviation. c The magnetic excitation spectrum along the q_HH direction in reciprocal space measured at T = 0.1 K, summed over 0 ≤ q_L ≤ 2 r.l.u. d The spinon spectrum obtained from tDMRG calculations for the XXZ model Eq. (1) with Δ = 2.6 on the 96-site chain. The continuum boundary (black lines) is the same as that shown in b for Δ = 2.6. e The dispersions of particle-like (red) and hole-like (black) spinons, symmetric about E = 0 in zero magnetic field, are sketched with the real Δ = 2.6 parameters for Yb₂Pt₂Pb. The bandwidth parameter I and the spinon gap Δ_S are indicated by arrows, with 2Δ_S the energy separation between the particle and hole bands at q_L = 0, 1, and 2 rlu