Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction

doi:10.1088/1674-1056/19/4/040512

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40512-040512.doi: 10.1088/1674-1056/19/4/040512

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction

王林成, 闫俊彦, 衣学喜

School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China

收稿日期:2009-09-02 修回日期:2009-09-29 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by National Natural Science Foundation of China (Grant Nos.~10847108 and 10775023).

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction

Wang Lin-Cheng(王林成) Yan Jun-Yan(闫俊彦), and Yi Xue-Xi(衣学喜)

School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China

Received:2009-09-02 Revised:2009-09-29 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by National Natural Science Foundation of China (Grant Nos.~10847108 and 10775023).

摘要/Abstract

摘要： We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya (DM) interaction, and investigate the effect of the DM interaction on the quantum phase transition (QPT) of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.

Abstract: We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya (DM) interaction, and investigate the effect of the DM interaction on the quantum phase transition (QPT) of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.

Key words: geometric phase, quantum phase transition, the Dzyaloshinski--Moriya interaction

中图分类号: (Quantized spin models, including quantum spin frustration)

75.10.Jm

75.10.Pq (Spin chain models) 03.67.-a (Quantum information) 03.65.Vf (Phases: geometric; dynamic or topological)

王林成, 闫俊彦, 衣学喜. Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction[J]. 中国物理B, 2010, 19(4): 40512-040512.

Wang Lin-Cheng(王林成) Yan Jun-Yan(闫俊彦), and Yi Xue-Xi(衣学喜). Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction[J]. Chin. Phys. B, 2010, 19(4): 40512-040512.

参考文献 47

[1]	Sachdev S 1999 Quantum Phase Transition} (Cambridge: Cambridge University Press)
[2]	Berry M V 1984 Proc. R. Soc. London A 392 45
[3]	Aharonov Y and Anandan J 1987 Phys. Rev. Lett. 58 1593
[4]	Samuel J and Bhandari R 1988 Phys. Rev. Lett. 60 2339
[5]	Mukunda N and Simon R 1993 Ann. Phys. (N.Y.) 228 205
[6]	Mukunda N and Simon R 1993 Ann. Phys. (N.Y.) 228 269
[7]	Pati A K 1995 Phys. Rev. A 52 2576
[8]	Sj?qvist E, Pati A K, Ekert A, Anandan J S, Erisson M, Oi D K L and Vedral V 2000 Phys. Rev. Lett. 85 2845
[9]	Bhandari R 2002 Phys. Rev. Lett. 89 268901
[10]	Anandan J 2002 Phys. Rev. Lett. 89 268902
[11]	Tong D M, Sj?qvist E, Kwek L C and Oh C H 2004 Phys. Rev. Lett. 93 080405
[12]	Carollo A C M and Pachos J K 2005 Phys. Rev. Lett. 95 157203
[13]	Zhu S L 2006 Phys. Rev. Lett. 96 077206
[14]	Chen G, Li J Q and Liang J Q 2006 Phys. Rev. A 74 054101
[15]	Ma Y Q and Chen S 2009 Phys. Rev. A 79 022116
[16]	Zanardi P and Paunkovi? N 2006 Phys. Rev. E 74 031123
[17]	Zanardi P, Quan H T, Wang X and Sun C P 2007 Phys. Rev. A 75 032109
[18]	Zhou H Q and Barjaktarevi? J P 2007 arXiv: 0701608 [cond-mat]
[19]	Campos Venuti L and Zanardi P 2007 Phys. Rev. Lett. 99 095701
[20]	Zanardi P, Giorda P and Cozzini M 2007 Phys. Rev. Lett. 99 100603
[21]	You W L, Li Y W and Gu S J 2007 Phys. Rev. E 76 022101
[22]	Osborne T J and Nielsen M A 2002 Phys. Rev. A 66 032110
[23]	Wu L A, Sarandy M S and Lidar D A 2004 Phys. Rev. Lett. 93 250404
[24]	Gu S J, Deng S S, Li Y Q and Lin H Q 2004 Phys. Rev. Lett. 93 086402
[25]	Cui H T, Song H S and Yu C S 2008 Chin. Phys. B 17 2795 2799
[26]	Cheng W W, Shan C J, Huang Y X, Li H and Liu T K 2008 Chin. Phys. B 17 4002 4008
[27]	Tong P Q and Zhu X 2008 Chin. Phys. B 17 1623
[28]	Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Phys. Rev. Lett. 96 140604
[29]	Yi X X, Cui H T and Wang L C 2006 Phys. Rev. A 74 054102
[30]	Yuan Z G, Zhang P and Li S S 2007 Phys. Rev. A 75 012102
[31]	Yi X X and Wang W 2007 Phys. Rev. A 75 032103
[32]	Wang L C, Huang X L and Yi X X 2008 Euro. Phys. J.} D 46 345 349
[33]	Li Y C and Li S S 2009 Phys. Rev. A 79 032338
[34]	Jafari R, Kargarian M, Langari A and Siahatgar M 2008 arXiv: 0804.4579 [cond mat]
[35]	Kargarian M, Jafari R and Langari A 2009 arXiv: 0903.0630 [quant ph]
[36]	Dzyaloshinskii I 1958 J. Phys. Chem. Solids 4 241
[37]	Moriya T 1960 Phys. Rev. Lett. 4 228
[38]	Moriya T 1960 Phys. Rev. 120 91
[39]	Anderson P W 1959 Phys. Rev. 115 2
[40]	Zhang G F 2007 Phys. Rev. A 75 034304
[41]	Gurkan Z N and Pashev O K 2008 arXiv: 0804.0710 [quant ph]
[42]	Kwan M K, Gurkan Z N and Kwek L C 2008 Phys. Rev. A 77 062311
[43]	Gao F, Tang S Q, Xie L J, Zhan X G and Zhang D Y 2009 Chin. Phys. B 18 3203
[44]	Lima J P, Goncalves L L and Alves T F A 2007 Phys. Rev. B 75 214406
[45]	Lima J P and Goncalves L L 2008 Phys. Rev. B 77 214424
[46]	Derzhko O, Verkholyak T, Krokhmalskii T and Büttner H 2006 Physica B 378 443
[47]	Cheng W W and Liu J M 2009 Phys. Rev. A 79 052320

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains: Effect of the Dzyaloshinski－Moriya interaction

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