  Aharonov-Bohm interferometry is the most direct probe of anyonic statistics
in the quantum Hall effect. The technique involves oscillations of the electric
current as a function of the magnetic field and is not applicable to Kitaev
spin liquids and other systems without charged quasiparticles. Here, we
establish a novel protocol, involving heat transport, for revealing fractional
statistics even in the absence of charged excitations, as is the case in
quantum spin liquids. Specifically, we demonstrate that heat transport in
Kitaev spin liquids through two distinct interferometer geometries, Fabry-Perot
and Mach-Zehnder, exhibits drastically different behaviors. Therefore, we
propose the use of heat transport interferometry as a probe of anyonic
statistics in charge insulators.
