Target space entanglement in quantum mechanics of fermions and matrices
- Resource Type
- article
- Authors
- Sotaro Sugishita
- Source
- Journal of High Energy Physics, Vol 2021, Iss 8, Pp 1-35 (2021)
- Subject
- Matrix Models
1/N Expansion
M(atrix) Theories
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
- Language
- English
- ISSN
- 1029-8479
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 1 3 $$ \frac{1}{3} $$ log N in the large N model. We obtain an analytical O N 0 $$ \mathcal{O}\left({N}^0\right) $$ expression of the mutual information for two intervals in the large N expansion.