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本文利用相干态正交化展开方法, 对两格点两电子Hubbard-Holstein极化子模型的能谱以及动力学特性进行了精确求解. 讨论了耦合强度g、平均声子数n以及电子 初态对纠缠演化特性及系统冯诺依曼熵的影响. 数值计算结果表明: 1)纠缠度随时间的演化呈现出良好的周期性, 当其他的参数固定时, 演化周期随耦合强度g增大逐渐减小, 与平均声子数n无关; 2)系统冯诺依曼熵同电子状态占有率表现出严格的同步演化特性; (3) 在弱耦合强度和低平均声子数下, 初始电子态c2+ c2+|Oe或c1+ c1+ |Oe较c1+c2+c1+ c2+具有更大的最大冯诺依曼熵, 并随耦合强度增大、平均声子数的增加而逐渐接近.
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关键词:
- 相干态正交化展开 /
- Hubbard-Holstein模型 /
- 极化子 /
- 场熵
We obtain the exact solution of energy spectrum and dynamics for the two-site Hubbard-Holstein model by the coherent states orthogonal expansion method. The influences of coupling strength g, the average number of phonons n and the initial electronic state on the evolution of system entanglement and von Neumann entropy are discussed. Numerical results are as follows. (a) Entanglement evolution with time shows a good periodicity. When the other parameters are fixed, the evolution period decreases as the coupling strength g goes up but it is independent of the average number of phonons n. (b) The von Neumann entropy of the system demonstrates strict synchronia with the electronic state occupancy probability. (c) Under the weak coupling strength and low average number of phonons, the initial electronic state c2+ c2+|Oe or c1+ c1+|Oe shows larger maximum von Neumann entropy during its evolution than that of c1+c2+c1+c2++ but they gradually approach to each other with the increase of coupling strength or average number of phonons.-
Keywords:
- coherent-state /
- orthogonalization expansion /
- Hubbard-Holstein model polaron /
- field entropy
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[15] Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023
[16] Obada A S F, Hessian H A, Abdel A M 2005 International Journal of Quantum Information 3 591
[17] Faisal A, El-Orany A, Wahiddin M R B, Obada A S F 2008 Optics Communications 281 2854
[18] Hu Y H, Fang M F, Liao X P 2006 Acta Optic Sinica 55 4631
[19] Zhang Y Y, Liu T, Chen Q H, Wang X G, Wang K L 2009 J. Phys. Condens. Matter 21 415601
[20] Zhang Y Y, Wang X G, Chen Q H 2009 Solid State Communications 149 2106
[21] Chaterjee J, Das A N 2000 Phys. Rev. B 61 4592
[22] Ren X Z, Jiang D L, Cong H L, Liao X 2009 Acta Phys. Sin. 58 5406 (in Chinese) [任学藻, 姜道来, 丛红璐, 廖旭 物理学报 2009 58 5406]
[23] Irish E K, Gea-Banacloche J, Martin I, Schwab K C 2006 Phys. Rev. B 72 195410
[24] Zhao Y, Zanardi P, Chen G H 2004 Phys. Rev. B 70 195113
[25] Yao K L, Li Y C, un X Z, Liu Q M, Qin Y, Fu H H, Gao G Y 2005 Phys. Lett. A 346 209
[26] Vladimir M, Stojanovic, Mihajlo Vanevic 2008 Phys. Rev. B 78 214301
[27] Phoenix S J D, Knight P L 1988 Annals of Physics 182 381
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[1] Fehske H,Wellein G, Loos J, Bishop A R 2008 Phys. Rev. B 77 085117
[2] Holstein T 1959 Ann. Phys. 8 325
[3] Das A N P, Choudhury S 1994 Phys. Rev. B 49 18
[4] Acquaroneet M 1998 Phys. Rev. B 58 7626
[5] Chatterjee J, Das A N, arXiv:cond-mat/0210607
[6] Ranninger J, Thibblin U 1992 Phys. Rev. B 45 7730
[7] deMello E V L, Ranninger J 1997 Phys. Rev. B 55 14872
[8] Berciu M 2007 Phys. Rev. B 75 081101
[9] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[10] Bouwmeaster D, Pan J W, Mattle K, Elbl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
[11] Bennett C H, Brassard G, Jozsa R, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[12] Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1996 Phys. Rev. Lett. 77 2818
[13] Shor P W 1995 Phys. Rev. A 52 2493
[14] Bardeen J, Cooper L N, Schrieffer J R 1957 Phys. Rev. 108 1175
[15] Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023
[16] Obada A S F, Hessian H A, Abdel A M 2005 International Journal of Quantum Information 3 591
[17] Faisal A, El-Orany A, Wahiddin M R B, Obada A S F 2008 Optics Communications 281 2854
[18] Hu Y H, Fang M F, Liao X P 2006 Acta Optic Sinica 55 4631
[19] Zhang Y Y, Liu T, Chen Q H, Wang X G, Wang K L 2009 J. Phys. Condens. Matter 21 415601
[20] Zhang Y Y, Wang X G, Chen Q H 2009 Solid State Communications 149 2106
[21] Chaterjee J, Das A N 2000 Phys. Rev. B 61 4592
[22] Ren X Z, Jiang D L, Cong H L, Liao X 2009 Acta Phys. Sin. 58 5406 (in Chinese) [任学藻, 姜道来, 丛红璐, 廖旭 物理学报 2009 58 5406]
[23] Irish E K, Gea-Banacloche J, Martin I, Schwab K C 2006 Phys. Rev. B 72 195410
[24] Zhao Y, Zanardi P, Chen G H 2004 Phys. Rev. B 70 195113
[25] Yao K L, Li Y C, un X Z, Liu Q M, Qin Y, Fu H H, Gao G Y 2005 Phys. Lett. A 346 209
[26] Vladimir M, Stojanovic, Mihajlo Vanevic 2008 Phys. Rev. B 78 214301
[27] Phoenix S J D, Knight P L 1988 Annals of Physics 182 381
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