The entanglement property in matrix product spin systems

  • 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 Sn 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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  • [1] Fannes M, Nachtergaele B, Werner R F. Commun. Math. Phys., 1992, 144: 4432 Verstraete F, Porras D, Cirac J I. Phys. Rev. Lett., 2004,93: 2272053 Garcia D P, Verstraete F, Wolf M M et al. arXiv: quantph/06081972v24 Asoudeh M, Karimipour V, Sadrolashra A. arXiv: quantph/0701160v55 Wolf M M, Ortiz G, Verstraete F et al. Phys. Rev. Lett.,2006, 97: 1104036 Asoudeh M, Karimipour V, Sadrolashra L A. Phys. Rev. B, 2007, 75: 2244277 Verstraete F, Cirac J I. arXiv: cond-mat/0505140; Osborne T J. arXiv: quant-ph/0508031; Hastings M B. arXiv:condmat/05085548 Greenberger D M, Horne M, Zeilinger A. Bell's Teorem, Quantum Theory and Conception of the Universe. Kluwer: Dordrecht, 19899 Briegel H J, Raussendorf R. Phys. Rev. Lett., 2001, 86:91010 A eck I, Kennedy T, Lieb E H et al. Commun. Math. Phys., 1988, 115: 47711 Klumper A, Schadschneider A, Zittartz J. J. Phys. A, 1991,24: L955; Z. Phys. B, 1992, 87: 28112 CAO Wan-Cang, LIU Dan, PAN Feng et al. Science in China Series G-Physics Mechanics Astron, 2006, 49(5): 60613 LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2010, 54: 825-828 (or arXiv: quant-ph/07053904)14 LIU Dan, ZHAO Xin, LONG Gui-Lu. Commun. Theor. Phys., 2008, 49: 32915 WU Hua, ZHAO Xin, LI Yan-Song et al. International Journal Of Quantum Information, 2010, 8(7): 1169-117716 Muralidharan S, Panigrahi P K. Phys. Rev. A, 2008, 77:03232117 Muralidharan S, Panigrahi P K. Phys. Rev. A, 2008, 78:06233318 Verstraete F, Cirac J I, Latorre J I et al. Phys. Rev. Lett.,2005, 94: 14060119 ZHU Jing-Min. Commun. Theor. Phys., 2010, 54(2): 373-37920 ZHU Jing-Min. Chin. Phys. Lett., 2008, 25(10): 3574-357721 ZHU Jing-Min. Chinese Physics C, 2011, 35(02): 144-14822 DONG Hui, LIU Xu-Feng, SUN Chang-Pu. Chinese Science Bulletin, 2010, 55(29): 3256-326023 AI Qing, WANG Ying-Dan, LONG Gui-Lu et al. Sci. China Ser. G, 2009, 52(12): 1898-190524 AI Qing, TAO Shi, LONG Gui-Lu et al. Phys. Rev. A,2008, 78: 022327
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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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The entanglement property in matrix product spin systems

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

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 Sn 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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