Entanglement statistics of randomly interacting spins

Abstract: We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can continuously interpolate between deterministic separable eigenstates and fully random entangled eigenstates, with non-trivial intermediate behavior. Entanglement strongly depends on the underlying topology of the interaction among the qubits. For a certain class of interactions GHZ entanglement is favoured by a non-separable collective interaction, while for fully separable pairwise interactions the ground states concentrate in the vicinity of W states.