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 $$ \frac{1}{3} $$
1
3
log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$
O
N
0
expression of the mutual information for two intervals in the large N expansion.
Entanglement area law in superfluid 4He