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Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain

Abstract

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. Here, by accurate absolute normalization of our inelastic neutron scattering data on a spin-1/2 Heisenberg antiferromagnetic chain compound, 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 experimental line shape resembles a rescaled two-spinon one with similar boundaries allows us to develop a simple picture for understanding multi-spinon excitations.

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Figure 1: Schematic representation of the magnetic excitations in a spin-1/2 (Heisenberg) antiferromagnetic chain and overview of the neutron scattering results for CuSO4·5D2O.
Figure 2: Excitations in the fully polarized state (μ0H = 5 T).
Figure 3: Excitations in zero magnetic field.
Figure 4: Sum rules.

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Acknowledgements

We acknowledge useful discussions with C. Broholm, B. Dalla Piazza, B. Fåk, B. Lake, C. Rüegg and A. Tennant. The work of M.M. was supported in part by US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award DE-FG02-08ER46544. M.E. acknowledges support from the Deutsche Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF), project 03KN5SAA. H.M.R. acknowledges support from the Swiss National Science Foundation (SNF) and the European Research Council (ERC). J-S.C. acknowledges support from the Foundation for Fundamental Research on Matter (FOM) and the Netherlands Organisation for Scientific Research (NWO).

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M.E. and H.M.R. performed the experiment with the help of A.S. on a crystal synthesized by A.K. Data treatment and fits were carried out by M.M., M.E. and H.M.R.; exact theoretical calculations were performed by J-S.C. The physical pictures for multi-spinon excitations were developed through various discussions between J-S.C and M.M., M.E. and H.M.R. M.E., M.M., J-S.C. and H.M.R. wrote the manuscript.

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Correspondence to Martin Mourigal.

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Mourigal, M., Enderle, M., Klöpperpieper, A. et al. Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain. Nature Phys 9, 435–441 (2013). https://doi.org/10.1038/nphys2652

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