Target space entanglement in quantum mechanics of fermions and matrices

Sotaro Sugishita

doi:10.1007/jhep08(2021)046

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arXiv · 2105.13726

Target space entanglement in quantum mechanics of fermions and matrices

Sotaro Sugishita

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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 $N\times N$ 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 $\mathcal{O}(N^0)$ expression of the mutual information for two intervals in the large $N$ expansion.

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Sotaro Sugishita. 2021-08-19. Target space entanglement in quantum mechanics of fermions and matrices. https://doi.org/10.1007/jhep08(2021)046

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