The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

doi:10.1088/1674-1056/22/9/090313

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 90313-090313.doi: 10.1088/1674-1056/22/9/090313

The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

钟鸣^a, 徐卉^a, 刘小贤^a, 童培庆^{a b}

a Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China;
b Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China

收稿日期:2012-12-19 修回日期:2013-03-27 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11205090 and 11175087) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJB140008).

The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

Zhong Ming (钟鸣)^a, Xu Hui (徐卉)^a, Liu Xiao-Xian (刘小贤)^a, Tong Pei-Qing (童培庆)^{a b}

a Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China;
b Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China

Received:2012-12-19 Revised:2013-03-27 Online:2013-07-26 Published:2013-07-26
Contact: Tong Pei-Qing E-mail:pqtong@njnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11205090 and 11175087) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJB140008).

摘要/Abstract

摘要： The effects of the Dzyaloshinski-Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ε_k of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log₂L (L is the length of a subchain) with the coefficient A≈1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ=0 and 0<h ≤1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.

关键词: Dzyaloshinskii-Moriya interaction, the XY chain in a transverse field, quantum entanglement, ground-state properties

Abstract: The effects of the Dzyaloshinski-Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ε_k of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log₂L (L is the length of a subchain) with the coefficient A≈1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ=0 and 0<h ≤1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.

Key words: Dzyaloshinskii-Moriya interaction, the XY chain in a transverse field, quantum entanglement, ground-state properties

中图分类号: (Entanglement measures, witnesses, and other characterizations)

03.67.Mn

75.10.Jm (Quantized spin models, including quantum spin frustration) 73.43.Nq (Quantum phase transitions) 75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.))

钟鸣, 徐卉, 刘小贤, 童培庆. The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field[J]. 中国物理B, 2013, 22(9): 90313-090313.

Zhong Ming (钟鸣), Xu Hui (徐卉), Liu Xiao-Xian (刘小贤), Tong Pei-Qing (童培庆). The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field[J]. Chin. Phys. B, 2013, 22(9): 90313-090313.

参考文献 42

[1]	Dzyaloshinshy I 1958 J. Phys. Chem. Solids 4 241
[2]	Moriya T 1960 Phy. Rev. 120 91
[3]	Seki S, Yamasaki Y, Soda M, Matsuura M, Hirota K and Tokura Y 2008 Phys. Rev. Lett. 100 127201
[4]	Li Q C, Dong S and Liu J M 2008 Phys. Rev. B 77 054442
[5]	Sergienko I A and Dagotto E 2006 Phys. Rev. B 73 094434
[6]	Oshikawa M and Affleck I 1997 Phys. Rev. Lett. 79 2883
[7]	Zhao J Z, Wang X Q, Xiang T, Su Z B and Yu L 2003 Phys. Rev. Lett. 90 207204
[8]	Kohgi M, Iwasa K, Mignot J M, Fak B, Gegenwart P, Lang M, Ochiai A, Aoki H and Suzuki T 2001 Phys. Rev. Lett. 86 2439
[9]	Veillette M Y, Chalker J T and Coldea R 2005 Phys. Rev. B 71 214426
[10]	Tsukada I, Takeya J T, Masuda T and Uchinokura K 2001 Phys. Rev. Lett. 87 127203
[11]	Messio L, Cepas O and Lhuillier C 2010 Phys. Rev. B 81 064428
[12]	Huh Y, Fritz L and Sachdev S 2010 Phys. Rev. B 81 144432
[13]	Wernsdorfer W, Stamatatos T C and Christou G 2008 Phys. Rev. Lett. 101 237204
[14]	Zakeri K, Zhang Y, Prokop J, Chuang T H, Sakr N, Tang W X and Kirschner J 2010 Phys. Rev. Lett. 104 137203
[15]	Jafari R, Kargarian M, Langari A and Siahatgar M 2008 Phys. Rev. B 78 214414
[16]	Jafari R and Langari A 2008 arXiv: 0812.1862v1[cond-mat.str-el]
[17]	Derzhko O, Verkholyak T, Krokhmalshii T and Büttner H 2006 Phys. Rev. B 73 214407
[18]	Verkholyak T, Derzhko O, Krokhmalskii T and Stolze J 2007 Phys. Rev. B 76 144418
[19]	Kádár Z and Zimborás Z 2010 Phys. Rev. A 82 032334
[20]	Kargarian M, Jafari R and Langari A 2009 Phys. Rev. A 79 042319
[21]	Li Y F and Kong X M 2013 Chin. Phys. B 22 037502
[22]	Chen T, Huang Y X, Shan C J, Li J X, Liu J B and Liu T K 2010 Chin. Phys. B 19 050302
[23]	Wang L C, Yan J Y and Yi X X 2010 Chin. Phys. B 19 040512
[24]	Liu B Q, Shao B, Li J, Zou J and Wu L A 2011 Phys. Rev. A 83 052112
[25]	Siskens T J, Capel H W and Gaemers K J F 1975 Physica 79A 259
[26]	Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 517
[27]	Wootters W 1998 Phys. Rev. Lett. 80 2245
[28]	Bennett C, Bernstein H, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
[29]	Osterloh A, Amico L, Falci G and Fazio R 2002 Nature 416 608
[30]	Pfeuty P 1970 Ann. Phys. 57 79
[31]	Zhong M and Tong P Q 2010 J. Phys. A: Math. Theor. 43 505302
[32]	Vidal G, Latorre J I, Rico E and Kitaev A 2003 Phys. Rev. Lett. 90 227902
[33]	Holzhey C, Larsen F and Wilczek F 1994 Nucl. Phys. B 424 443
[34]	Lieb E, Schultz T and Mattis D 1961 Ann. Phys. 16 407
[35]	Tong P Q and Liu X X 2006 Phys. Rev. Lett. 97 017201
[36]	Kawamura H 1988 Phys. Rev. B 38 4916
[37]	Stolze J, Viswanath V S and Müller G 1992 Z. Phys. B 89 45
[38]	de Oliveira T R, Miranda E, Rigolin G and de Oliveira M C 2008 Phys. Rev. A 77 032325
[39]	Barouch E and McCoy B 1971 Phys. Rev. A 3 786
[40]	McCoy B, Barouch E and Abraham D 1971 Phys. Rev. A 4 2331
[41]	Müller G and Shrock R 1985 Phys. Rev. B 32 5845
[42]	Keating J P and Mezzadri F 2004 Commun. Math. Phys. 252 543

The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

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