Dissipationless dynamics of randomly coupled spins at high temperatures

TL;DR

This paper introduces a method to analyze high-frequency spin correlators in disordered spin systems, revealing exponential decay and low-frequency noise effects relevant for superconducting circuits at millikelvin temperatures.

Contribution

The authors develop a novel technique for computing high-frequency asymptotics of spin correlators in disordered systems, linking microscopic dynamics to observable noise phenomena.

Findings

Spin correlators decay exponentially at high frequencies.

Strongly coupled spin pairs act as two-level systems causing low-frequency noise.

Results apply to understanding susceptibility and flux noise in superconducting circuits.

Abstract

We develop a technique to compute the high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the dynamical spin correlator decreases exponentially at high frequencies, $< SS>_{\omega}\sim\exp(-\tau_{*}\omega)$ and compute the characteristic time $\tau^{*}$ of this dependence. In a typical random configuration, some fraction of spins form strongly coupled pairs, which behave as two-level systems. Their switching dynamics is driven by the high-frequency noise from the surrounding spins, resulting in low-frequency $1/f$ noise in the magnetic susceptibility and other physical quantities. We discuss application of these results to the problem of susceptibility and flux noise in superconducting circuits at mK temperatures.