$1/f^\alpha$ noise in interacting spin systems: a real space RG approach

Localized paramagnetic electrons are believed to be the cause of magnetic flux noise that plagues superconducting qubits, but how such interacting spins generate frequency dependent noise of the form $1/f^\alpha$ is not well understood. We describe a novel real space RG procedure that is equipped to calculate directly various dynamical quantities in a strongly disordered Heisenberg spin system (in arbitrary dimensions), including the `noise' from such systems. In 1-D, we find that the RG procedure describes a fairly temperature-indepedent noise with a power law $\alpha < 1$ that varies smoothly depending on the disorder strength, relative concentration of Ferro/Anti-Ferro bonds and temperature. The dynamic structure factor (of spin-spin correlations) inherits this power law while displaying a crossover to a related power at higher frequencies. In 2-D, the RG results in dynamics that are diffusive at high temperatures but remain anomalous at lower temperatures. A possible connection of the phenomena of $1/f$ noise and Many-Body Localization is also discussed.