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

MARCOS GAUDIANO, OMAR OSENDA Y GUIDO RAGGIO

Physical Review A

American Physical Society

Lugar: Nueva York, Estados Unidos; Año: 2008 p. 221091 - 221097

1050-2947

We consider the two-spin-subsystem entanglement for eigenstates of the Hamiltonian $H=sum_{1leqj< kleq N} left( rac{1}{r_{j,k}} ight)^{alpha}sigma_j cdot sigma_k$ for a ring of $N$ $spin-1/2$ particles with associated spin vector operator $hbar/ 2 sigma_j$ for the $j^th$ spin. Here $r_{j,k}$ is the chord distance between sites $j$ and $k$. The case $alpha=2$ corresponds to the solvable Haldane-Shastry model whose spectrum has very high degeneracies not present for $alpha eq 2$. Two-spin-subsystem entanglement shows high sensitivity and distinguishes $alpha= 2$ from $alpha eq 2$. There is no entanglement beyond nearestneighbors for all eigenstates when $alpha=2$. Whereas for $alpha eq 2$ 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 $alpha$.