Target space entanglement in quantum mechanics of fermions and matrices

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 Renyi entropies are N log 2 for N particles or an N x 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 1/3 log N in the large N model. We obtain an analytical O(N-0) expression of the mutual information for two intervals in the large N expansion.