Entanglement in SU(2)-invariant quantum spin systems
John Schliemann · Physical Review A · 2003
We analyze the entanglement of SU(2)-invariant density matrices of two spins ${S}_{1},$ ${S}_{2}$ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic-spin systems. The partial transpose of such a state has the same multiplet structure and degeneracies as the original matrix with the eigenvalue of largest multiplicity being non-negative. The case ${S}_{1}=S,$ ${S}_{2}=1/2$ can be solved completely and is discussed in detail with respect to isotropic Heisenberg spin models. Moreover, in this case the Peres-Horodecki criterion turns out to be a sufficient condition for nonseparability. We also characterize SU(2)-invariant states of two spins of length 1.