  In this paper, we study the entanglement structure of mixed states in quantum
many-body systems using the $\textit{negativity contour}$, a local measure of
entanglement that determines which real-space degrees of freedom in a subregion
are contributing to the logarithmic negativity and with what magnitude. We
construct an explicit contour function for Gaussian states using the fermionic
partial-transpose. We generalize this contour function to generic many-body
systems using a natural combination of derivatives of the logarithmic
negativity. Though the latter negativity contour function is not strictly
positive for all quantum systems, it is simple to compute and produces
reasonable and interesting results. In particular, it rigorously satisfies the
positivity condition for all holographic states and those obeying the
quasi-particle picture. We apply this formalism to quantum field theories with
a Fermi surface, contrasting the entanglement structure of Fermi liquids and
holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi
liquids show anomalous temperature dependence of the negativity depending on
the dynamical critical exponent. We further compute the negativity contour
following a quantum quench and discuss how this may clarify certain aspects of
thermalization.
