Bipartite entanglement in spin-1/2 Heisenberg model

HU Ming-Liang; TIAN Dong-Ping

doi:10.1088/1674-1137/32/4/013

Chinese Physics C> 2008, Vol. 32> Issue(4) : 303-307 DOI: 10.1088/1674-1137/32/4/013

Bipartite entanglement in spin-1/2 Heisenberg model

HU Ming-Liang ^, ,
TIAN Dong-Ping

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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]^1/2if 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>Δ_c (Δ_c=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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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Bipartite entanglement in spin-1/2 Heisenberg model

Corresponding author: HU Ming-Liang,

Received Date: 2007-07-16

Accepted Date: 2007-11-16

Available Online: 2008-04-05

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]^1/2if 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>Δ_c (Δ_c=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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Bipartite entanglement in spin-1/2 Heisenberg model

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