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Register a new userStructure of end states for a Haldane Spin Chain
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Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in Y_2BaNi_{1-x}Mg_xO_5. At finite fields, there is a Zeeman resonance below the Haldane gap. The wave vector dependence of its intensity provides direct evidence for staggered magnetization at chain ends, which decays exponentially towards the bulk (xi = 8(1) at T=0.1K). Continuum contributions to the chain end spectrum indicate inter-chain-segment interactions. We also observe a finite size blue shift of the Haldane gap.
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This paper overviews the behavior of the end-chain spins of linear chain systems possessing a Haldane gap. The physical properties of the end-chain spins are described by reviewing the results obtained primarily with materials known as NENP, Ni(C2H8N2)2NO2(ClO4), and NINAZ, Ni(C3H10N2)2N3(ClO4).
We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system CsNiCl3. Measurements over a wide range of wave-vector transfers along the chain confirm that above T_N CsNiCl3 is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length xi=4.0(2) sites at T=6.2K. This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperature, suggesting that the correlations perpendicular to the chain direction and associated with the interchain coupling lower the single-chain correlation length. A multi-particle continuum is observed in the quantum-disordered phase in the region in reciprocal space where antiferromagnetic fluctuations are strongest, extending in energy up to twice the maximum of the dispersion of the well-defined triplet excitations. We show that the continuum satisfies the Hohenberg-Brinkman sum rule. The dependence of the multi-particle continuum on the chain wave-vector resembles that of the two-spinon continuum in antiferromagnetic spin-1/2 Heisenberg chains. This suggests the presence of spin-1/2 degrees of freedom in CsNiCl3 for T < 12K, possibly caused by multiply-frustrated interchain interactions.
We consider the one-dimensional spin chain for arbitrary spin $s$ on a periodic chain with $N$ sites, the generalization of the chain that was studied by Blume and Capel cite{bc}: $$H=sum_{i=1}^N left(a (S^z_i)^2+ b S^z_iS^z_{i+1}right).$$ The Hamiltonian only involves the $z$ component of the spin thus it is essentially an Ising cite{Ising} model. The Hamiltonian also figures exactly as the anisotropic term in the famous model studied by Haldane cite{haldane} of the large spin Heisenberg spin chain cite{bethe}. Therefore we call the model the Blume-Capel-Haldane-Ising model. Although the Hamiltonian is trivially diagonal, it is actually not always obvious which eigenstate is the ground state. In this paper we establish which state is the ground state for all regions of the parameter space and thus determine the phase diagram of the model. We observe the existence of solitons-like excitations and we show that the size of the solitons depends only on the ratio $a/b$ and not on the number of sites $N$. Therefore the size of the soliton is an intrinsic property of the soliton not determined by boundary conditions.
We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modelling of the dynamical response demonstrates our complete quantitative understanding of these states.
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