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Sudden death of entanglement in fermionic systems under collective decoherence

We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin $3/2$ interacting with a global bosonic environment. We resort to an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare its dynamics with that of a pair of distinguishable qubits immersed in the same environment. According to the system's initial state, three types of qualitatively different dynamics are identified: i) \textit{invariant regime}, corresponding to initial states that belong to a decoherence free subspace (DFS), which maintain invariant their entanglement and coherence throughout the evolution; ii) \textit{exponential decay}, corresponding to initial states orthogonal to the DFS, and evolve towards states whose entanglement and coherence decrease exponentially; iii) \textit{entanglement sudden death}, corresponding to initial states that have some overlap with the DFS and exhibit a richer dynamics leading, in particular, to the sudden death of the fermionic entanglement, while the coherence decays exponentially. Our analysis offers insights into the dynamics of entanglement in open systems of identical particles, into its comparison with the distinguishable-party case, and into the existence of decoherence free subspaces and entanglement sudden death in indistinguishable-fermion systems.