Entanglement across a transition to quantum chaos

We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-$1∕2$ lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures—namely, the reduced von Neumann entropy and the concurrence—and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.