Linear entropy fails to predict entanglement behavior in low-density fermionic systems

Entanglement is considered a fundamental ingredient for quantum technologies, while condensed matter systems are among the good candidates for the development of practical devices for quantum processing. For bipartite pure states the von Neumann entropy is a proper measure of entanglement, while the linear entropy, associated to the mixedness of the reduced density matrices, is a simpler quantity to be obtained and is considered to be qualitatively equivalent to the von Neumann. Here we investigate both linear and von Neumann entropies for quantifying entanglement in homogeneous, superlattice and disordered Hubbard chains. We find that for low densities systems (n less than or similar to 0.6) the linear entropy fails in reproducing the qualitative behavior of the von Neumann entropy. This then may lead to incorrect predictions (i) of maximum and minimum entanglement states and (ii) of quantum phase transitions.