Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Parton Fermi Surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua {~\textit{et~al.}}, Ref. [arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/r^{3}$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.