We analyze the entanglement of SU(2)-invariant density matrices of two spins $\vec S_{ 1}$, $\vec S_{ 2}$ 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 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 ciriterion turns out to be a sufficient condition for non-separability. We also characterize SU(2)-invariant states of two spins of length 1.
Categories: quant-ph cond-mat