Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain material CuSO$_4$.5D$_2$O

One of the simplest quantum many-body systems is the spin-1/2 Heisenberg antiferromagnetic chain, a linear array of interacting magnetic moments. Its exact ground state is a macroscopic singlet entangling all spins in the chain. Its elementary excitations, called spinons, are fractional spin-1/2 quasiparticles created and detected in pairs by neutron scattering. Theoretical predictions show that two-spinon states exhaust only 71\% of the spectral weight and higher-order spinon states, yet to be experimentally located, are predicted to participate in the remaining. By accurate absolute normalization of our inelastic neutron scattering data on the spin-1/2 Heisenberg antiferromagnetic chain compound CuSO$_4$.5D$_2$O, we account for the full spectral weight to within 99(8)\% [1]. Our data thus establish and quantify the existence of higher-order spinon states. The observation that, within error bars, the experimental line shape resembles a rescaled two-spinon one with similar boundaries allows us to develop a simple picture for understanding multi-spinon excitations. \\[4pt] [1] Nature Physics {\bf 9}, 435--441 (2013)