Target space entanglement in quantum mechanics of fermions and matrices

• URL: http://arxiv.org/abs/2105.13726v2
• Date: Thu, 19 Aug 2021 13:00:10 GMT
• Title: Target space entanglement in quantum mechanics of fermions and matrices
• Authors: Sotaro Sugishita
• Abstract summary: We consider entanglement of first-quantized identical particles by adopting an algebraic approach. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We obtain an analytical $mathcalO(N0)$ expression of the mutual information for two intervals in the large $N$ expansion.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 R\'enyi 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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