1 / f α noise and generalized diffusion in random Heisenberg spin systems
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CitationAgarwal, Kartiek, Eugene Demler, and Ivar Martin. 2015. “1/Fαnoise and Generalized Diffusion in Random Heisenberg Spin Systems.” Physical Review B 92 (18). https://doi.org/10.1103/physrevb.92.184203.
AbstractWe study the "flux-noise" spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor S-q(f), at finite wave vector q, exhibits a power-law behavior both at high and low frequencies f, with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at T = 0 and T = infinity. The low-frequency power-law behavior of the structure factor is inherited by any generic probe with a finite bandwidth and is of the form 1/f(alpha) with 0.5 < alpha < 1. An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings. More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusion which directly follows from a generalized spin-diffusion propagator. We also argue that 1/f-noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional 1/f(alpha) behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce 1/f(alpha) noise in SQUIDs.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41412194
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