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Entanglement in SU(2)-invariant quantum spin systems

John Schliemann
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Abstract

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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John Schliemann. 2003-07-12. Entanglement in SU(2)-invariant quantum spin systems. https://doi.org/10.1103/physreva.68.012309

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