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84988791953
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note
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z is the soliton width, and d is the soliton-soliton distance. We have checked that this form gives results very similar to the sinusoidal form, which has been used throughout this paper.
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84988781991
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The individual gaps of the finite-size clusters actually increase as δ→0. However, a finite-size scaling analysis shows that in the thermodynamic limit the spin gap decreases monotonously as δ is lowered from 1 to 0.
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P. A. Fleury and R. Loudon, Phys. Rev. 166, 514 (1968). The Raman operator may also contain alternating contributions, similar to the δ term in the Hamiltonian. We have verified that the inclusion of such a contribution modifies our results (Fig. 4) only slightly. For the sake of simplicity, we therefore stick with the easiest possible Raman operator in this paper.
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84988794723
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note
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Terms in the Raman operator which commute with the Hamiltonian contribute to a featureless peak at zero frequency. In the limit δ=0, the full spin Hamiltonian is proportional to the Raman operator, leading to a trivial Raman response: I(ω) = δ(ω). Here we are interested in the nontrivial features of I(ω) away from ω=0 at finite δ.
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41
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84988788818
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note
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Typically, a set of poles with decreasing weights for the higher-energy poles is indicative of an emerging continuum. This is the case for the three major poles at higher energies in the Raman spectra at zero field, whereas the lowest pole becomes an isolated bound state as N→∞.
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42
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0000006185
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V. N. Muthukumar, C. Gros, W. Wenzel, R. Valenti, P. Lemmens, B. Eisener, and G. Güntherodt, M. Weiden, C. Geibel, and F. Steglich, Phys. Rev. B 54, R9635 (1999).
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44
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84988794702
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note
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z/N for the finite lattice (shown in Fig. 5).
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-
-
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45
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85088351024
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note
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-(k).
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46
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0031558202
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