The entanglement property in matrix product spin systems

ZHU Jing-Min

doi:10.1088/1674-1137/36/4/003

Chinese Physics C> 2012, Vol. 36> Issue(4) : 311-315 DOI: 10.1088/1674-1137/36/4/003

The entanglement property in matrix product spin systems

ZHU Jing-Min

College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

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We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We nd that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy S_n of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.

References

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ZHU Jing-Min. The entanglement property in matrix product spin systems[J]. Chinese Physics C, 2012, 36(4): 311-315. doi: 10.1088/1674-1137/36/4/003

ZHU Jing-Min. The entanglement property in matrix product spin systems[J]. Chinese Physics C, 2012, 36(4): 311-315. doi: 10.1088/1674-1137/36/4/003 shu

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Received: 2011-07-19
Revised: 2011-07-28

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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

The entanglement property in matrix product spin systems

College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Received Date: 2011-07-19

Accepted Date: 2011-07-28

Available Online: 2012-04-05

Abstract: We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We nd that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy S_n of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.

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