Abstract
We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as \( \frac{1}{3} \) log N in the large N model. We obtain an analytical \( \mathcal{O}\left({N}^0\right) \) expression of the mutual information for two intervals in the large N expansion.
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Sugishita, S. Target space entanglement in quantum mechanics of fermions and matrices. J. High Energ. Phys. 2021, 46 (2021). https://doi.org/10.1007/JHEP08(2021)046
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DOI: https://doi.org/10.1007/JHEP08(2021)046