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77957978963
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For small s in S, charge disorder can lead to rare regions where (locally) the spin gap becomes negative, reflecting the tendency to isolated islands with weak magnetic order. For simpliCity, we do not take into account this weak magnetic condensate in our calculation, as it will influence the excitation spectrum only at the very lowest energies. Hence, we simply ignore the few eigenmodes of S + Sψ with negative eigenvalues.
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The spectral weights of χ′′(q,ω) of Refs. [10, 29, 31] were incorrect due to errors in the numerical evaluation of certain matrix elements. As a result, the weights need to be corrected by an energy-dependent (but only weakly momentum-dependent) factor which is roughly given by 1/ω. Thus, the weight distribution in constant-energy scans remains unaffected. The results of Ref. [31] can be found in correct form in: T. Ulbricht, Diploma thesis, Karlsruhe 2004 (unpublished).
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In all figures, u1 = -1. 15, u2 = 0. 1, c1, 2; x, y = 0. 2, w = 0. 05, v = 0. 2 in S, c = 100 meV, s = 70 meV in S, λ1 = λ3/2 = 50 meV/{pipe}{pipe}typ, λ2 = λ4 = 0 in Sψ unless otherwise noted. In contrast, Ref. [10] used s = 120 meV in S, resulting in a significantly larger spin gap [37].
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