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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.
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Keywords:
- coherent-state /
- orthogonalization expansion /
- Hubbard-Holstein model polaron /
- field entropy
[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 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 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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