Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain

Abstract

Assemblies of interacting quantum particles often surprise us with properties that are difficult to predict. 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; they are created and detected in pairs by neutron scattering. Theoretical predictions show that two-spinon states exhaust only 71% of the spectral weight while higher-order spinon states, yet to be experimentally located, are predicted to participate in the remaining. Here, by accurate absolute normalization of our inelastic neutron scattering data on a compound realizing the model, we account for the full spectral weight to within 99(8)%. Our data thus establish and quantify the existence of higher-order spinon states. The observation that within error bars, the entire weight is confined within the boundaries of the two-spinon continuum, and that the lineshape resembles a rescaled two-spinon one, allow us to develop a simple physical picture for understanding multi-spinon excitations.Comment: 22 pages, 4 figures, Supplementary material