Entanglement in SU(2)-invariant quantum spin systems

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.

5 pages

References in corpus (2)

• Entanglement in quantum critical phenomena
• Macroscopic entanglement jumps in model spin systems

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