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A fermionic disordered one dimensional wire in the presence of attractiveinteractions is known to have two distinct phases: A localized and asuperconducting one depending on the strength of interaction and disorder. Thelocalized region may also exhibit a metallic behaviour if the system size isshorter than the localization length. Here we show that the superconductingphase has a distinct distribution of the entanglement entropy and entanglementspectrum distinct from the metallic regime. The entanglement entropydistribution is strongly asymmetric with L\'evy alpha stable distribution(compared to the Gaussian metallic distribution), and the entanglement levelspacing distribution is unitary (compared to orthogonal). Thus, entanglementproperties may reveal properties which can not be detected by other methods.

Entanglement properties and quantum phases for a fermionic disordered one dimensional wire with attractive interactions