  Topological phases of matter possess intricate correlation patterns typically
probed by entanglement entropies or entanglement spectra. In this work, we
propose an alternative approach to assessing topologically induced edge states
in free and interacting fermionic systems. We do so by focussing on the
fermionic covariance matrix. This matrix is often tractable either analytically
or numerically and it precisely captures the relevant correlations of the
system. By invoking the concept of monogamy of entanglement we show that highly
entangled states supported across a system bi-partition are largely
disentangled from the rest of the system, thus appearing usually as gapless
edge states. We then define an entanglement qualifier that identifies the
presence of topological edge states based purely on correlations present in the
ground states. We demonstrate the versatility of this qualifier by applying it
to various free and interacting fermionic topological systems.

Strongly Correlated Electrons;Quantum Physics