1 / f α noise and generalized diffusion in random Heisenberg spin systems
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![FIG. 4. Scaled dynamical structure factor (a) S˜0q(˜ω) = x1/2−1/β S0q(ωx1/β ) at T = 0, (b) ˜S∞q (˜ω) = x−1/β S∞q (ωx1/β ) at T = ∞for q ∈ 2π/[40(yellow), 80(cyan), 120(green), 400(blue), 800(red)], and x = (2π/40)/q; the results shown correspond to a syst](https://thumb-us.123doks.com/thumbv2/123dok_us/7901626.188085/7.612.59.561.52.211/scaled-dynamical-structure-factor-yellow-results-shown-correspond.webp)
![FIG. 5. (a) The T(is plotted as a function of frequency for variousωcies. (c) = ∞ dynamical structure factor S∞q (ω) q = 2π/ll ∈ [40, 800]), system size L = 15000](https://thumb-us.123doks.com/thumbv2/123dok_us/7901626.188085/16.612.69.284.184.584/plotted-function-frequency-variouswcies-dynamical-structure-factor-size.webp)
![FIG. 14.Various features of the simulations on two-βdimensional system of size 50×50 are shown.(a)The noise spectrum for low frequencies has a power lawtail Sq(ω) ∼ 1/√ω (q = (π, π) here); (b) The distribu-tion of gaps is fairly broad; (c) The fidelity f does notrise over the course of RG; (d) Approximate scaling col-lapse using the Generalized-diffusion ansatz using exponent= 0.55±0.05 for wave-vectors q = (2πn/L, 2πn/L) with n ∈[2(blue), 4(red), 6(magenta), 8(cyan), 10(black), 12(green)].](https://thumb-us.123doks.com/thumbv2/123dok_us/7901626.188085/20.612.71.283.49.342/features-simulations-bdimensional-frequencies-delity-approximate-generalized-diusion.webp)
![FIG. 17. (a) The inverse participation ratio is finite [seen byscaling with system sizesand(dashed line fit); (b) spin-wave peak seen in the structurefactor(red line fit corresponds tocorresponds to L = 500 (yellow), L = 1000 (blue) L = 2000 (red) ] and scales with frequency as IPR(ω) ∼ ω Sq(ω); (c) the peak occurs at frequency ωc(q) ∼ q2 q1.95); (d) the width (calculatedas inverse height of the peak) scales as Γ(q) ∼ q2 (red line fit q2.2)](https://thumb-us.123doks.com/thumbv2/123dok_us/7901626.188085/21.612.333.543.49.400/participation-byscaling-structurefactor-corresponds-tocorresponds-frequency-frequency-calculatedas.webp)
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