Entropy of Non-Abelian Anyons from Slow Quasiparticle Dynamics in Quantum Hall Interferometers

Abstract

Non-Abelian anyons emerging in fractional quantum Hall states carry a characteristic entropy, $ΔS = k_B \log d$, where $d$ is the anyon's quantum dimension. This $\mathcal{O}(1)$ entropy can, in principle, be extracted from charge measurements of an antidot via Maxwell relations. However, equilibrium charge measurements in fractional antidots have proven to be challenging with conventional charge detectors. Here, we propose a scheme based on an antidot embedded in an interferometer, in which the charge can be inferred from the recently observed time-dependent switching of the interference phase. Performing such non-local charge measurements at equilibrium, the characteristic $\mathcal{O}(1)$ entropy of non-Abelian anyons (e.g., $d = \sqrt{2}$ for the $ν= 5/2$ state) can be extracted for intermediate temperatures, which exceed the level spacing of the interferometer edge, but are much smaller than the level spacing of the antidot.