Two-spin-subsystem entanglement in spin-1/2 rings with long-range interactions

MARCOS GAUDIANO, OMAR OSENDA, GUIDO RAGGIO

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMERICAN PHYSICAL SOCIETY

Año: 2008 vol. 77 p. 221091 - 221097

1050-2947

We consider the two-spin-subsystem entanglement for eigenstates of the Hamiltonian H=1j<kN()j·k for a ring of N spin-1/2 particles with associated spin vector operator (/2)j for the jth spin. Here rj,k is the chord distance between sites j and k. The case =2 corresponds to the solvable Haldane-Shastry model whose spectrum has very high degeneracies not present for 2. Two-spin-subsystem entanglement shows high sensitivity and distinguishes =2 from 2. There is no entanglement beyond nearest neighbors for all eigenstates when =2. Whereas for 2 one has selective entanglement at any distance for eigenstates of sufficiently high energy in a certain interval of which depends on the energy. The ground state (which is a singlet only for even N) does not have entanglement beyond nearest neighbors, and the nearest-neighbor entanglement is virtually independent of the range of the interaction controlled by .