Two-spin-subsystem entanglement in spin-1/2 rings with long-range interactions
M. Gaudiano, O. Osenda, and G. A. Raggio

We consider the two-spin subsystem entanglement for eigenstates of the Hamiltonian \[ H= \sum_{1\leq j&lt k \leq N} \left( \frac{1}{r_{j,k}}\right)^{\alpha} {\mathbf \sigma}_j\cdot {\mathbf \sigma}_k \] for a ring of $N$ spins $1/2$ with asssociated spin vector operator $(\hbar /2){\bf \sigma}_j$ for the $j$-th spin. Here $r_{j,k}$ is the chord-distance betwen sites $j$ and $k$.\\ The case $\alpha =2$ corresponds to the solvable Haldane-Shastry model whose spectrum has very high degeneracies not present for $\alpha \neq 2$. Two spin subsystem entanglement shows high sensistivity and distinguishes $\alpha =2$ from $\alpha \neq 2$. There is no entanglement beyond nearest neighbors for all eigenstates when $\alpha =2$. Whereas for $\alpha \neq 2$ one has selective entanglement at any distance for eigenstates of sufficiently high energy in a certain interval of $\alpha$ 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 $\alpha$.

© 2008 The American Physical Society.