  We study non-analytic behavior in the static charge susceptibility in finite
density states of the ABJM theory using its holographic dual. Emphasis is
placed on a particular state characterized by vanishing entropy density at zero
temperature, and Fermi surface-like singularities in various fermionic
correlation functions. The susceptibility exhibits branch points in the complex
momentum plane, with a real part quantitatively very similar to the location of
the Fermi surface singularities.
