Chiral symmetry breaking, entanglement, and the nucleon spin decomposition

The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-$N_c$ limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy.

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