Entanglement in SU(2)-invariant quantum spin systems

Details Entanglement in SU(2)-invariant quantum spin systems Entanglement in SU(2)-invariant quantum spin systems

2002-12-19

arxiv.org/abs/quant-ph/0212114v3

Phys. Rev. A 68, 012309 (2003)

Physics

Quantum Physics

5 pages

Scientific paper

10.1103/PhysRevA.68.012309

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.

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