Bipartite entanglement in spin-1/2 Heisenberg model

  • The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ-1, and it may keep a steady value of 0.5 in the region of B<J[(Δ+1)2-γ2]1/2 if Δ>γ-1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δcc=γ-1 and (γ2-1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.

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HU Ming-Liang and TIAN Dong-Ping. Bipartite entanglement in spin-1/2 Heisenberg model[J]. Chinese Physics C, 2008, 32(4): 303-307. doi: 10.1088/1674-1137/32/4/013
HU Ming-Liang and TIAN Dong-Ping. Bipartite entanglement in spin-1/2 Heisenberg model[J]. Chinese Physics C, 2008, 32(4): 303-307.  doi: 10.1088/1674-1137/32/4/013 shu
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Received: 2007-07-16
Revised: 2007-11-16
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Bipartite entanglement in spin-1/2 Heisenberg model

    Corresponding author: HU Ming-Liang,

Abstract: 

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ-1, and it may keep a steady value of 0.5 in the region of B<J[(Δ+1)2-γ2]1/2 if Δ>γ-1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δcc=γ-1 and (γ2-1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.

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