Bera, A.K.; Lake, B.; Essler, E.H.L; Vanderstraeten, L.; Hubig, C.; Schollwöck, U.; Islam, A.T.M.N.; Schneidewind, A.; Quintero-Castro, D.L.: Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet. Physical Review B 96 (2017), p. 054423/1-16
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Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and, as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain spatially anisotropic magnetic insulators. These can be thought of in terms of weakly coupled chains of spins S = 1/2, and a spin flip thus carries integer spin S = 1. The collective excitations in these systems, called spinons, turn out to carry fractional spin quantum number S = 1/2. Interestingly, at sufficiently low temperatures the weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinon-confinement process in the quasi-one-dimensional, spin-1/2 antiferromagnet with Heisenberg-Ising (XXZ) anisotropy SrCo2V2O8. A wide temperature range both above and below the long-range ordering temperature TN = 5.2 K is explored. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. These are based on a description in terms of a one-dimensional, S = 1/2 XXZ antiferromagnetic spin chain, where the interchain couplings are modeled by an effective staggered magnetic mean field. A wide range of exchange anisotropies are investigated and the parameters specific to SrCo2V2O8 are identified. Recently developed theoretical technique based on tangent-space matrix product states gives a very complete description of the data and provides good agreement not onlywith the energies of the bound modes but also with their intensities.We also successfully explain the effect of temperature on the excitations including the experimentally observed thermally induced resonance between longitudinal modes below TN and the transitions between thermally excited spinon states above TN. In summary, our work establishes SrCo2V2O8 as a beautiful paradigm for spinon confinement in a quasi-one-dimensional quantum magnet and provides a comprehensive picture of this process.