Chinese Physics B ( First Published in 1992 )

Chinese Physics B ( First published in 1992 )

Published monthly in hard copy by the Chinese Physical Society and online by IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK Institutional subscription information: 2013 volume For all countries, except the United States, Canada and Central and South America, the subscription rate is £977 per annual volume. Single-issue price £97. Delivery is by air-speeded mail from the United Kingdom. Orders to: Journals Subscription Fulﬁlment, IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK For the United States, Canada and Central and South America, the subscription rate is US$1930 per annual volume. Single-issue price US$194. Delivery is by transatlantic airfreight and onward mailing. Orders to: IOP Publishing, PO Box 320, Congers, NY 10920-0320, USA ⃝c 2013 Chinese Physical Society and IOP Publishing Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright owner. Supported by the National Natural Science Foundation of China, the China Association for Science and Technology, and the Science Publication Foundation, Chinese Academy of Sciences Editorial Oﬃce: Institute of Physics, Chinese Academy of Sciences, PO Box 603, Beijing 100190, China Tel: (86 – 10) 82649026 or 82649519, Fax: (86 – 10) 82649027, E-mail: [email protected] 主管单位: 中国科学院国内统一刊号: CN 11–5639/O4 主办单位: 中国物理学会和中国科学院物理研究所广告经营许可证：京海工商广字第0335号承办单位: 中国科学院物理研究所编辑部地址: 北京中关村中国科学院物理研究所内主编：欧阳钟灿通讯地址: 100190 北京 603 信箱出版：中国物理学会 Chinese Physics B 编辑部印刷装订：北京科信印刷厂电话: (010) 82649026, 82649519 编辑: Chinese Physics B 编辑部传真: (010) 82649027 国内发行: Chinese Physics B 出版发行部 E-mail: [email protected] 国外发行: IOP Publishing Ltd “Chinese Physics B”网址: 发行范围: 公开发行 http://cpb.iphy.ac.cn(编辑部) 国际统一刊号: ISSN 1674–1056 http://iopscience.iop.org/cpb (IOP) Published by the Chinese Physical Society 顾顾顾问问问 Advisory Board 陈佳洱教授, 院士 Prof. Academician Chen Jia-Er 北京大学物理学院, 北京 100871 School of Physics, Peking University, Beijing 100871, China 冯端教授, 院士 Prof. Academician Feng Duan 南京大学物理系, 南京 210093 Department of Physics, Nanjing University, Nanjing 210093, China 黄祖洽教授, 院士 Prof. Academician Huang Zu-Qia 北京师范大学低能核物理研究所, Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 北京 100875 100875, China 李政道教授, 院士 Prof. Academician T. D. Lee Department of Physics, Columbia University, New York, NY 10027, USA 李荫远研究员, 院士 Prof. Academician Li Yin-Yuan 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 丁肇中教授, 院士 Prof. Academician Samuel C. C. Ting LEP3, CERN, CH-1211, Geneva 23, Switzerland 杨振宁教授, 院士 Prof. Academician C. N. Yang Institute for Theoretical Physics, State University of New York, USA 杨福家教授, 院士 Prof. Academician Yang Fu-Jia 复旦大学物理二系, 上海 200433 Department of Nuclear Physics, Fudan University, Shanghai 200433, China 周光召研究员, 院士 Prof. Academician Zhou Guang-Zhao (Chou Kuang-Chao) 中国科学技术协会, 北京 100863 China Association for Science and Technology, Beijing 100863, China 王乃彦研究员, 院士 Prof. Academician Wang Nai-Yan 中国原子能科学研究院, 北京 102413 China Institute of Atomic Energy, Beijing 102413, China 梁敬魁研究员, 院士 Prof. Academician Liang Jing-Kui 中国科学院物理研究所, 北京 100190 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

(Continued ) Chin. Phys. B Vol. 22, No. 9 (2013) 090313

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), and 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 19 December 2012; revised manuscript received 27 March 2013)

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 εk 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 log2 L (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.

Keywords: Dzyaloshinskii–Moriya interaction, the XY chain in a transverse ﬁeld, quantum entanglement, ground-state properties PACS: 03.67.Mn, 75.10.Jm, 73.43.Nq, 75.40.Cx DOI: 10.1088/1674-1056/22/9/090313

1. Introduction correlations[24] of the one-dimensional XY chain in a transverse field were studied. Unfortunately, the authors used in- In recent years, the antisymmetric Dzyaloshinskii– correct excitation spectra, which brought doubts to their re- Moriya (DM) interaction has received much attention. The sults. In fact, the excitation spectra and the critical points of DM interaction introduced by Dzyaloshinskii[1] and Moriya[2] the anisotropic XY chain with the DM interaction were firstly is a combination of super-exchange and spin–orbital in- found by Siskens et al.,[25] however the properties of the ex- teractions, which can provide the microscopic mechanism citation spectra did not arouse enough attention. It should be for the coexistence of ferroelectricity and incommensurate noticed that the excitation spectra εk of this model are not sym- magnetism in many multiferroics.[3–5] Some quantum anti- metrical in the momentum space and are not always greater ferromagnetic systems are described by the DM interac- than zero, which may cause some special behaviors of the sys- tion with underlying helical magnetic structures, such as Cu tem. benzoate,[6,7] Yb As ,[8] Cs CuCl ,[9] BaCu Si O ,[10] and 4 3 2 4 2 2 7 On the other hand, quantum entanglement is viewed as a [11,12] kagome antiferromagnets. Other materials, such as an Fe main ingredient in quantum information processes and has at- double layer and a wheel single-molecule magnet, have also tracted considerable interest in various fields of physics. In the [13,14] been studied with the DM interaction. last decade, much attention has been paid to the relationship Besides those real materials, one-dimensional spin between quantum entanglement and quantum phase transitions chains with the DM interaction have also been studied (QPTs) (see Ref. [26] for a review). There are two widely [15–23] extensively. For example, the phase diagram of the used measures of entanglement for spin systems. One is the Ising model (without external field) with the DM interaction concurrence,[27] and the other is the von Neumann entropy.[28] was studied with the quantum renormalization-group (QRG) By using the concurrence, Osterloh et al.[29] found that for method, in which a quantum critical point separates the anti- the anisotropic XY chain in a transverse field, the derivative ferromagnetic phase and the chiral phase.[15] The phase di- of the nearest-neighbor concurrence presents a logarithmic diagram of the XXZ model with the DM interaction was also vergence for an infinite system in the vicinity of the critical obtained with the QRG approach; three phases (ferromag- point h = 1, which is related to the critical properties of the netic, spin-fluid, and Neel phases) were found.[16] The dy- Ising transition.[30] For the same model, we found that[31] the namic properties of the XXZ and the XY chains with the DM derivative of the nearest-neighbor concurrence changes little interaction have also been studied.[17,18] Very recently, the with the increasing system size N in the vicinity of the critical effects of the DM interaction on the quantum and classical point γ = 0 (0 < h ≤ 1) corresponding to the anisotropy transi- ∗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). †Corresponding author. E-mail: [email protected] © 2013 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 090313-1 Chin. Phys. B Vol. 22, No. 9 (2013) 090313 tion. And Vidal et al. found that[32] the von Neumann entropy by the Bogoliubov transformation

SL is a constant in the noncritical region and SL ∼ (clog2 L)/3 c = u + v∗ † . (5) at the critical points. The coefficient is given by the central k kηk −kη−k p charge c in the conformal field theory,[33] c = 1/2 at h = 1 αk − βk uk = q = cosθk, while c = 1 at = 0 (0 < h ≤ 1). However, for the anisotropic p γ 2(βk − αk βk) XY chain in a transverse field with the DM interaction, the for- iγ sink mulas used to calculate the concurrence and the von Neumann vk = = i sinθk, (6) q p entropy should be both improved, which results from the char- 2(βk − αk βk) acteristics of the excitation spectra. We will study the effects 2 2 2 with αk = cosk + h and βk = α + γ sin k. of the DM interaction on the entanglement of this model in k detail. The paper is organized as following. In Section 2, the 3 model is given. In Section 3, we obtain the detailed phase diagram by analytical and numerical methods. In Section 4, we 2 k

discuss the behaviors of entanglement. A brief conclusion is ε given in Section 5. 1

2. Model 0

The Hamiltonian of the XY chain with the DM interaction -3 -2 -1 0 1 2 3 (in the z direction) in a transverse field reads[17] k Fig. 1. Two typical excitation spectra. The solid and dashed lines cor- N 1 + γ 1 − γ respond to D = 0.2, γ = 0.2, h = 0.5 and D = 0.2, γ = 0.5, h = 0.5, H = − σ xσ x + σ yσ y + hσ z ∑ n n+1 n n+1 n respectively. The dotted line corresponds to εk = 0. n=1 2 2 N x y y x The forms of uk and vk are independent of D and the − ∑ D(σn σn+1 − σn σn+1), (1) n=1 same as those in the XY model without the DM interaction. But the excitation spectra ε are not symmetrical in the mo- where N is the number of spins in the chain, γ (−1 ≤ γ ≤ 1) k mentum space and not always greater than zero. Figure 1 is the anisotropy parameter of the system, D is the strength shows two typical examples, in which ε are positive for all of the DM interaction, σ x,y,z are the Pauli matrices, and h is a k k when D = 0.2, γ = 0.5, h = 0.5, while they are negative for uniform external transverse field. 1.7 < k < 2.4 when D = 0.2, γ = 0.2, h = 0.5. In the ther- By using the Jordan–Wigner transformation,[34] Hamilto- † modynamic limit (N → ∞), the ground state |Gi of the system nian (1) can be written with spinless fermion operators cn and corresponds to the configuration in which all states with εk < 0 cn, which yields are filled and those with εk ≥ 0 are empty, that is N † † † |Gi = 0, ( ≥ 0), H = − {[(1 + 2iD)c cn+1 + γc c ηk εk ∑ n n n+1 † (7) n=1 ηk |Gi = 0, (εk < 0). N † +hcncn] + h.c.} + ∑ h. (2) The |Gi can be written as |Gi = ∏ Gk, and Gk can be derived n=1 k>0 † from the transformation ηk = ukck + v−kc−k Through Fourier transforms of the fermionic operators, c = √ n −ikn G = cosθ |0i |0i + i sinθ |1i |1i , (ε ≥ 0), ∑k ck e / N (here k = 2pπ/N for odd N and periodic k k k −k k k −k k (8) boundary condition or for even N and antiperiodic bound- Gk = |1ik|0i−k, (εk < 0), ary condition, p = −(N − 1)/2, −(N − 3)/2, ..., (N − 3)/2, with |0ik and |1ik corresponding to the vacuum and the occu- (N − 1)/2), Hamiltonian (2) can be written in the momentum pied states of ck, respectively. space and be reduced to the diagonal form It must be pointed out that the above ground state is very

π different from that used in Ref. [24] coming from incorrect † H = ∑ εk(ηk ηk − 1/2) (3) excitation spectra, where εk are always larger than or equal to k=−π zero. Furthermore, because εk may be negative, the formulas with[25] used to calculate the correlation functions, the concurrence, and the von Neumann entropy should be modiﬁed, which will q 2 2 2 εk = −4Dsink + 2 (cosk + h) + γ sin k (4) be discussed in detail in the following. 090313-2 Chin. Phys. B Vol. 22, No. 9 (2013) 090313

3. Phase diagram corresponds to γ = 2D, and the curved solid line corresponds p to h = 4D2 − γ2 + 1. In view of the symmetry of Hamiltonian (1), here we con- (iii) D ≥ 0.5. The γ is always smaller than 2D for γ ≤ 1, sider the case of γ, D, h ≥ 0. We use the general Lee–Yang p so the points from h = 0 to h = 4D2 − γ2 + 1 are all critical method[35] to ﬁnd critical points. According to this method, points . The phase diagram is showed in Fig. 3(c). The curved we solve equation εk(h) = 0 in a complex h plane. The solu- p solid line also corresponds to h = 4D2 − γ2 + 1. tions at the positive real axis correspond to the QPT points. From excitation spectra (4), the solution of ε (h) = 0 in a k 0.4 complex h plane is (a)

p 0.2 h = −cosk + 4D2 − γ2 sink. (9) 0

Three cases can be discussed. h ) Im( (i) D = 0, which corresponds to the XY chain in a trans- -0.2 verse ﬁeld. Equation (9) can be transformed to h = −cosk + -0.4 iγ sink. There are two distinct critical lines, the line h = 1 and -1.0 -0.5 0 0.5 1.0 Re(h) the line segment h ∈ (0,1) with γ = 0. The phase diagram is 0.4 shown in Fig. 3(a). As it is well known, region I corresponds (b) to a ferromagnetic (FM) phase ordered along the x direction 0.2 (FMx), while region II corresponds to a disordered paramagnetic (PM) phase. Following the standard notation, we refer to 0 the QPT across the critical line h = 1 driven by the transverse h ) Im( magnetic ﬁeld as the Ising transition, and the QPT across the -0.2 critical line γ = 0 driven by the anisotropy parameter γ as the -0.4 anisotropy transition. -1.0 -0.5 0 0.5 1.0 Re(h) (ii) 0 < D < 0.5. If γ > 2D, Eq. (9) can be transformed p 2 2 Fig. 2. The solution of εk(h) = 0 in the complex h plane with (a) γ = 0.5 to h = −cosk + i γ − 4D sink. It is easy to check that the or (b) γ = 0.05. Here D = 0.2. solutions, which lie on an ellipse, are cutting the positive real axis at h = 1 in the complex h plane (see Fig. 2(a)). If γ ≤ In the above three cases, εk > 0 for all k in regions I and II, p 2 2 2D, Eq. (9) can be written as h = −cosk + 4D − γ sink. while εk < 0 for more than one k in region III. Obviously, re- The solutions are always real and the maximal value is h = gion III may correspond to a special phase. Because the phase p 4D2 − γ2 + 1, so they are all critical points from h = 0 to diagram shown in Fig. 3(b) contains most of the phases, as p h = 4D2 − γ2 + 1 (see Fig. 2(b)). The phase diagram is long as we make clear the properties of this phase diagram, shown in Fig. 3(b), which is composed of three regions. Re- the properties of the other will also be understood. Therefore, gions I and II are noncritical regions with an energy gap, while in this paper, we focus on the study of the QPTs in the case of region III is a critical region without an energy gap. The ver- 0 < D < 0.5. In the following calculations, we take D = 0.2 tical solid line corresponds to h = 1, the horizontal solid line without loss of generality.

1.0 1.0 1.0 (a) (b) (c)

0.8 0.8 0.8 II I 0.6 0.6 0.6 III

γ I II

II γ γ 0.4 0.4 0.4

0.2 0.2 III 0.2

0 0 0 0 0.5 1.0 1.5 0 0.5 1.0 1.5 0 0.5 1.0 1.5 h h h Fig. 3. The phase diagrams for (a) D = 0, (b) D = 0.2, and (c) D = 0.5. Regions I, II, and III between the solid lines and coordinate axes p correspond to FM, PM, and chiral phases, respectively. The dashed lines in region I of panels (a) and (b) correspond to h = 1 − γ2, p while the dotted lines in region III of panels (b) and (c) correspond to h = 4D2 − 2γ2 + 1, which are discussed in Section 4. 090313-3 Chin. Phys. B Vol. 22, No. 9 (2013) 090313

In order to study the properties of each phase of this are x x x x model, we study correlation function CL = C1,N/2 = hσ1 σN/2i and the chiral order parameter in the z direction[36] Gln = hBlAni = −hAnBli 1 = sgn(− )cos[(n − l)k − 2 ], (13) 1 N ∑ εk θk x y y x N k Ch = ∑ hσi σi+1 − σi σi+1i. (10) 4N i=1 x Usually, the phase with CL 6= 0 is referred to as the FM hAlAni = −hBlBni phase ordered along the x direction, while the phase with 2i − ∑ Θ(ε )sin(n − l)k, n 6= l, x = N k k (14) CL = 0 is referred to as the PM phase. And the phase with 1, n = l, Ch 6= 0 is referred to as the chiral phase. For this model, the chiral order parameter is where θk are deﬁned in Eq. (6). In regions I and II, 1 C = Θ(ε )sink, (11) h N ∑ k k hAlAni = −hBlBni = δln, (15) where as εk are greater than zero for all k. Because hAlAli and hBlBli 1, x ≥ 0, Θ(x) = never occur, 0, x < 0.

G1,2 G1,3 ... G1,n Obviously, Ch = 0 in regions I and II where εk are always pos- x . . . . itive. C1,n = . . . . . (16) x However, the correlation function CL should be discussed Gn−1,2 Gn−1,3 ... Gn−1,n in detail. From the Jordan–Wigner transformation,[34] we have In region III, εk may be negative for some k , thus hAlAni x x x [37] C1,n = hσ1 σn i = hB1A2B2A3 ...Bn−1Ani, (12) and hBlBni are nonzero even if n 6= l. Therefore,

† † with An = c + cn and Bn = c − cn. This can be calculated x 1/2 n n C1,n = (U) , (17) by using the Wick theorem in terms of the products of the expectation values of just two operators. The basic contractions where

0 hB1A2i hB1B2i hB1A3i ... hB1Ani

−hB1A2i 0 hA2B2i hA2A3i ... hA2Ani

U = −hB1B2i −hA2B2i 0 hB2A3i ... hB2Ani . (18)

...... 0 ......

−hB1Ani −hA2Ani ...... 0

x Figure4 gives CL as a function of h for different γ. We 0.08 can ﬁnd that from region I to region II with γ > 2D (the solid x 0.06 line), CL continuously decreases to zero at h = 1, and from re- x gion III to region II with γ < 2D (the dashed line), CL is always 0.04 h

zero. C 0.02 1.0 0 0.8 0 0.2 0.4 0.6 0.8 1.0 γ 0.6 x L Fig. 5. Chiral order parameter C as a function of γ. The solid and C h 0.4 dashed lines correspond to h = 0.8 and 1.02, respectively. Here D = 0.2.

0.2 Figure5 gives Ch as a function of γ for different h. We can 0 find that from region III to region I with h < 1 (the solid line), C continuously decreases to zero at = 2D. From region III 0 0.5 1.0 1.5 h √ γ h to region II with 1 < h < 1 + 4D2 (the dashed line), C con- √ h x tinuously decreases to zero at γ = 4D2 − h2 + 1. The non- Fig. 4. Correlation function CL as a function of h. The solid and dashed lines correspond to γ = 0.5 and 0.2, respectively. Here D = 0.2. x analytic points of CL and Ch do agree with the critical points 090313-4 Chin. Phys. B Vol. 22, No. 9 (2013) 090313 found by the Lee–Yang method (see Fig. 3(b)). where rn are the square roots of the eigenvalues of the operator According to the above numerical results, we can find that y y ∗ y y x R = ρi j(σ ⊗ σ )ρi j(σ ⊗ σ ) (20) in region I, CL 6= 0 and Ch = 0, which corresponds to the FM x h → phase along the axis. When 0, there are two degen- in decreasing order. Due to the symmetry of the Hamiltonian, erate ferromagnetic ground states with all spins pointing ei- the density matrix ρi j has the form ther parallel or antiparallel to the x axis, | →→→ ··· →i or x  a a  | ←←← ··· ←i. In region II, CL = 0 and Ch = 0, which cor- 11 0 0 14 0 a a 0 responds to the PM phase. When h 1, the ground state is a ρ =  22 23 . (21) i j  0 a∗ a 0  paramagnet | ↑↑↑ ··· ↑i with all spins polarized up along the  23 33  a∗ 0 0 a x 14 44 z axis. While in region III, CL = 0 and Ch 6= 0, which corresponds to the chiral phase induced by the DM interaction. A The matrix elements can be expressed in terms of the various classical picture[15] for this phase is that the spins orientate in correlation functions the xy plane and the angle between neighboring spins has a 1 a = (1 + 2hσ zi + hσ zσ zi), nonzero value. It is worth mention that different from the FM 11 4 i i j 1 and the PM phases, the chiral phase is gapless. a = a = (1 − hσ zσ zi), 22 33 4 i j 1 a = (1 − 2hσ zi + hσ zσ zi), 4. Quantum entanglement 44 4 i i j 1 x x y y x y y x In order to acquire a better understanding of the effects a14 = [hσ σ i − hσ σ i − i(hσ σ i + hσ σ i)], 4 i j i j i j i j of the DM interaction on the ground-state entanglement, we 1 a = [hσ xσ xi + hσ yσ yi + i(hσ xσ yi − hσ yσ xi)]. (22) study the concurrence and the Von Neumann entropy in this 23 4 i j i j i j i j section. It should be noticed that for the XY chain in a transverse field without the DM interaction, the Hamiltonian is real, 4.1. Concurrence ∗ ρi j = ρi j, therefore the imaginary parts of a14 and a23 are zero. Concurrence measures the entanglement between two While for the XY chain in a transverse field with the DM inter- spins and is calculated with the density matrix ρi j obtained action, Hamiltonian (1) is complex, the imaginary parts of a14 from the ground-state wave function in which all the spins and a23 are no longer zero. except those at positions i and j have been traced out. The Now we turn to discuss the behaviors of concurrence concurrence between sites i and j is defined as across those three critical lines in Fig. 3(b). In this paper, the nearest-neighbor concurrence C12 of sites 1 and 2 is consid- Ci j = max{0,r1 − r2 − r3 − r4}, (19) ered.

0.3 0.3 (a) (c) (e)

0.2 0.2 0.2

C 0.1 0.1 0.1

a b c 0 0 0 0 0.5 1.0 1.5 0 0.5 1.0 1.5 0 0.4 0.8 6 cp cp (b) (d) 2 (f) 2 1 3 1

D / h D / h 0

D / h

D C D C 0 D C 0 -1

-2 cp -1 -3 0 0.5 1.0 1.5 0 0.5 1.0 1.5 0 0.4 0.8 h h γ

Fig. 6. The C12 as a function of h for (a) γ = 0.5 and (c) γ = 0.2. (e) The C12 as a function of γ for h = 0.8. Panels (b), (d), and (f) are the derivatives of the curves in panels (a), (c), and (e), respectively. Here D = 0.2, cp represents the critical point. 090313-5 Chin. Phys. B Vol. 22, No. 9 (2013) 090313

g iG Figure6 gives C12 and its derivative. Because the forms T = jl jl . jl −iG g of uk and vk in Eq. (6) are independent of D and εk > 0 for all l j jl k in regions I and II, all the results of the correlation functions Here, G jl are also defined by Eq. (13) and in Eq. (22) are the same as those of the XY model without π 1 −sgn(ε )ik( j−l) the DM interaction. Therefore, the behaviors of C12 and its g = e k . jl N ∑ derivative in the vicinity of the critical point from region I to k=−π region II (see Figs. 6(a) and 6(b) for γ = 0.5) are related to the We should note that when D = 0, g jl = δ jl and εk ≥ 0 for [29] critical properties of the Ising transition. However for the all k. When D 6= 0, εk may be negative in some regions, so g jl cases from region III to region II (see Figs. 6(c) and 6(d) for are no longer equal to δ jl γ = 0.5) and from region III to region I (see Figs. 6(e) and 6(f)  1, if j = l, for h = 0.8), the derivative of C12 hardly changes with increas-  π g jl = ing N in the vicinity of the critical point and these behaviors ∑ −isgn(εk)sin[k( j − l)], if j 6= l.  k=−π are like the critical properties of the anisotropy transition.[31] j 6= l g In addition, there are some other nonanalytic points, such However, we find that when , jl are pure imaginary num- bers and g jl = −gl j, so the 훤N matrix is an antisymmetric ma- as points a, b, and c in Fig. 6 corresponding to C12 = 0. For trix. the XY chain in a transverse field without the DM interaction, p 2 [38] Secondly, considering L spins at sites 1,2, ..., L, we can C12 = 0 occurs at h = 1 − γ , which was first found by get a 2L × 2L submatrix 훤 from 훤 by eliminating the rows Barouch and McCoy.[39,40] Furthermore, Muller¨ et al. found L N and columns corresponding to those spins belong to the rest of that at this boundary the ground state can be expressed as a the chain. Obviously, 훤 is also antisymmetrical and can be product state.[41] The ground state is in fact doubly degener- L always brought into a block-diagonal form ated. This boundary is shown as a dashed line in Fig. 3(a). And the DM interaction may also affect this boundary. For γ > 2D, T L−1 0 1 p 훤 L = 푄훤 푄 = 퐼 + ⊕n=0 iνn , νn ≥ 0. (26) it still satisfies h = 1 − γ2, which is shown as a dashed line −1 0 in Fig. 3(b). But for 0 < γ < 2D, we find by numerical fitting Here, 푄 is an orthogonal matrix, and 퐼 is a unit matrix. There- p 2 2 that C12 = 0 at h ≈ 4D − 2γ + 1, which is shown as dotted fore, the von Neumann entropy is given by[42] lines in Figs. 3(b) and 3(c). L−1 1 + ν j 1 + ν j SL = ∑ − log2 4.2. Von Neumann entropy j=0 2 2 Von Neumann entropy measures the entanglement be- 1 − ν 1 − ν − j log j . (27) tween a block of L contiguous spins and the rest of the chain, 2 2 2 [42] which is defined as We find that the behaviors of the von Neumann entropy are similar in the same phase, so without loss of generality we SL = −Tr(ρL log2 ρL). (23) only give SL at some typical points in Fig.7. In regions I (the

Here, ρL is the reduced density matrix obtained from the solid line in Fig. 7(a)) and II (the dashed line in Fig. 7(a)), SL ground-state wave function in which all the spins except ﬁrst is a non-zero constant when the block is large enough. Differ-

L contiguous spins have been traced out. ently, in region III, SL is proportional to log2 L with the coeffi- Following the standard procedure,[42] firstly, we consider cient A ≈ 1/3 (the dashed and dotted lines in Fig. 7(b)), which two Majorana operators m2l and m2l+1 for each site l of the is the same as that of the XY chain in a transverse field without N-spin chain, which are defined as the DM interaction for γ = 0 and 0 < h ≤ 1, so the whole region represents the critical property. In the critical line h = 1, l−1 l−1 z x z y SL is proportional to log L with the coefficient A ≈ 1/6 (the m2l+1 = ∏ σ j σl , m2l = ∏ σ j σl . (24) 2 j=0 j=0 solid line in Fig. 7(b)), which is the same as that in the Ising transition line of the XY chain in a transverse field without the The operators mn are Hermitian and obey the anticommutation DM interaction. relation {m j,ml} = 2δ jl. In the ground state, the correlation Especially, on the dashed line of Fig. 3(b), where the re- matrix with the expectation values hm jmli is a 2N ×2N matrix p lationship between h and γ satisfies h = 1 − γ2 for γ > 2D, written as there is SL = 1 and the ground state is doubly degenerated.  T T ... T  11 12 1N For example, the result of SL at the point (h,γ) = (0.866,0.5)  . . . .  훤N =  . . . . , is shown as a dotted line in Fig. 7(a). However, for 0 < γ < 2D, p 2 2 TN1 TN2 ... TNN SL ∼ (log2 L)/3, even if h = 4D − 2γ + 1 (the dotted line (25) in Fig. 7(b)) while C12 = 0. 090313-6 Chin. Phys. B Vol. 22, No. 9 (2013) 090313

1.2 excitation spectra which are not symmetrical in the momen- (a) tum space and are not always positive. 1.0 Acknowledgment

L 0.8 We thank Li Wen-Juan and Xiong Ye for useful discus- S sions.

0.6 References [1] Dzyaloshinshy I 1958 J. Phys. Chem. Solids 4 241 0.4 [2] Moriya T 1960 Phy. Rev. 120 91 0 10 20 30 40 50 [3] Seki S, Yamasaki Y, Soda M, Matsuura M, Hirota K and Tokura Y 2008 L Phys. Rev. Lett. 100 127201 3.0 [4] Li Q C, Dong S and Liu J M 2008 Phys. Rev. B 77 054442 (b) [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 2.0 [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

L [9] Veillette M Y, Chalker J T and Coldea R 2005 Phys. Rev. B 71 214426 S [10] Tsukada I, Takeya J T, Masuda T and Uchinokura K 2001 Phys. Rev. Lett. 87 127203 1.0 [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 0 [14] Zakeri K, Zhang Y, Prokop J, Chuang T H, Sakr N, Tang W X and 1 2 3 4 5 6 Phys. Rev. Lett. log L Kirschner J 2010 104 137203 2 [15] Jafari R, Kargarian M, Langari A and Siahatgar M 2008 Phys. Rev. B Fig. 7. (a) The SL as a function of L in noncritical regions. The solid, 78 214414 dashed, and dotted lines correspond to the points h = 0.5, 1.1, 0.866 [16] Jafari R and Langari A 2008 arXiv: 0812.1862v1 [cond-mat.str-el] with D = 0.2, γ = 0.5, respectively. (b) The SL as a function of log2 L. [17] Derzhko O, Verkholyak T, Krokhmalshii T and Buttner¨ H 2006 Phys. The solid, dashed, and dotted lines correspond to the points in the Ising Rev. B 73 214407 transition line at h = 1.0, γ = 0.5 and in region III at γ = 0.2, h = 0.5, [18] Verkholyak T, Derzhko O, Krokhmalskii T and Stolze J 2007 Phys. p h = 4D2 − 2γ2 + 1 = 1.039 for D = 0.2, respectively. Rev. B 76 144418 [19] Kad´ ar´ Z and Zimboras´ Z 2010 Phys. Rev. A 82 032334 Therefore, under the effects of the DM interaction, the [20] Kargarian M, Jafari R and Langari A 2009 Phys. Rev. A 79 042319 critical behaviors of the XY chain for 0 < γ < 2D and 0 < h ≤ [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. p 2 2 4D − γ + 1 are similar to that of the XY chain in a trans- Phys. B 19 050302 verse field without the DM interaction for γ = 0 and 0 < h ≤ 1. [23] Wang L C, Yan J Y and Yi X X 2010 Chin. Phys. B 19 040512 And the properties of the chiral phase are distinctively differ- [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 ent from the FM and PM phases, where SL is always a non- [26] Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 zero constant. 517 [27] Wootters W 1998 Phys. Rev. Lett. 80 2245 [28] Bennett C, Bernstein H, Popescu S and Schumacher B 1996 Phys. Rev. 5. Conclusion A 53 2046 [29] Osterloh A, Amico L, Falci G and Fazio R 2002 Nature 416 608 In summary, we have studied the effects of the DM in- [30] Pfeuty P 1970 Ann. Phys. 57 79 teraction on the ground-state properties of the XY chain in a [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 transverse field. By the analytical and numerical results we 227902 find that (i) a gapless chiral phase is induced by the DM in- [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 teraction for γ < 2D; (ii) from the chiral phase to the FM (or [35] Tong P Q and Liu X X 2006 Phys. Rev. Lett. 97 017201 PM) phase , the QPTs are like those in the anisotropy transi- [36] Kawamura H 1988 Phys. Rev. B 38 4916 [37] Stolze J, Viswanath V S and Muller¨ G 1992 Z. Phys. B 89 45 tion; (iii) the von Neumann entropy SL in the chiral phase is [38] de Oliveira T R, Miranda E, Rigolin G and de Oliveira M C 2008 Phys. proportional to log2 L with the coefficient A ≈ 1/3, which is Rev. A 77 032325 the same as that of the XY chain in a transverse field without [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 the DM interaction for γ = 0 and 0 < h ≤ 1. Moreover, the [41] Muller¨ G and Shrock R 1985 Phys. Rev. B 32 5845 above ground-state properties mainly attribute to the special [42] Keating J P and Mezzadri F 2004 Commun. Math. Phys. 252 543

090313-7 Chinese Physics B

Volume 22 Number 9 September 2013

TOPICAL REVIEW — Magnetism, magnetic materials, and interdisciplinary research

097501 Crystal structures, phase relationships, and magnetic phase transitions of R5M4 compounds (R = rare earths, M = Si, Ge) Ouyang Zhong-Wen and Rao Guang-Hui 097503 Using magnetic nanoparticles to manipulate biological objects Liu Yi, Gao Yu and Xu Chenjie

TOPICAL REVIEW — Low-dimensional nanostructures and devices 096104 Topological insulator nanostructures and devices Xiu Fa-Xian and Zhao Tong-Tong 096803 Intercalation of metals and silicon at the interface of epitaxial graphene and its substrates Huang Li, Xu Wen-Yan, Que Yan-De, Mao Jin-Hai, Meng Lei, Pan Li-Da, Li Geng, Wang Ye-Liang, Du Shi-Xuan, Liu Yun-Qi and Gao Hong-Jun 097202 Electrostatic ﬁeld effects on three-dimensional topological insulators Yang Wen-Min, Lin Chao-Jing, Liao Jian and Li Yong-Qing 097305 Metallic nanowires for subwavelength waveguiding and nanophotonic devices Pan Deng, Wei Hong and Xu Hong-Xing 097306 Proximity effects in topological insulator heterostructures Li Xiao-Guang, Zhang Gu-Feng, Wu Guang-Fen, Chen Hua, Dimitrie Culcer and Zhang Zhen-Yu 098105 Preparing three-dimensional graphene architectures: Review of recent developments Zeng Min, Wang Wen-Long and Bai Xue-Dong 098106 Graphene applications in electronic and optoelectronic devices and circuits Wu Hua-Qiang, Linghu Chang-Yang, Lu¨ Hong-Ming and Qian He 098107 Unique electrical properties of nanostructured diamond cones Gu Chang-Zhi, Wang Qiang, Li Jun-Jie and Xia Ke 098108 Controllable growth of low-dimensional nanostructures on well-deﬁned surfaces Qin Zhi-Hui 098109 Controllable synthesis of fullerene nano/microcrystals and their structural transformation induced by high pressure Yao Ming-Guang, Du Ming-Run and Liu Bing-Bing 098505 Field-effect transistors based on two-dimensional materials for logic applications Wang Xin-Ran, Shi Yi and Zhang Rong

(Continued on the Bookbinding Inside Back Cover) RAPID COMMUNICATION

094209 Horizontally slotted photonic crystal nanobeam cavity with embedded active nanopillars for ultrafast direct modulation Wang Da, Cui Kai-Yu, Feng Xue, Huang Yi-Dong, Li Yong-Zhuo, Liu Fang and Zhang Wei 096801 Interaction and local magnetic moments of metal phthalocyanine and tetraphenylporphyrin molecules on noble metal surfaces Song Bo-Qun, Pan Li-Da, Du Si-Xuan, and Gao Hong-Jun + 3+ 097801 Effects of Li on photoluminescence of Sr3SiO5: Sm red phosphor Zhang Xin, Xu Xu-Hui, Qiu Jian-Bei and Yu Xue

GENERAL

090201 Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz–Ladik– Lattice system Fu Jing-Li, Song Duan, Fu Hao, He Yu-Fang and Hong Fang-Yu 090202 Pinning consensus analysis of multi-agent networks with arbitrary topology Ji Liang-Hao, Liao Xiao-Feng and Chen Xin 090203 Simultaneous identification of unknown time delays and model parameters in uncertain dynamical systems with linear or nonlinear parameterization by autosynchronization Gu Wei-Dong, Sun Zhi-Yong, Wu Xiao-Ming and Yu Chang-Bin 090204 Analysis of variable coefficient advection diffusion problems via complex variable reproducing kernel particle method Weng Yun-Jie and Cheng Yu-Min 090205 Feedback control scheme of traffic jams based on the coupled map car-following model Zhou Tong, Sun Di-Hua, Zhao Min and Li Hua-Min 090206 Ultra-elongated depth of focus of plasmonic lenses with concentric elliptical slits under Gaussian beam illumination Wang Jing and Fu Yong-Qi 090301 Pseudoscalar Cornell potential for a spin-1/2 particle under spin and pseudospin symmetries in 1 + 1 dimension M. Hamzavi and A. A. Rajabi 090302 Thermal vacuum state for the two-coupled-oscillator model at finite temperature: Derivation and application Xu Xue-Xiang, Hu Li-Yun, Guo Qin and Fan Hong-Yi 090303 Detaching two single-mode squeezing operators from the two-mode squeezing operator Fan Hong-Yi and Da Cheng 090304 Analysis of vibrational spectra of nano-bio molecules: Application to metalloporphrins K Srinivasa Rao, G Srinivas, J. Vijayasekhar, V. U. M. Rao, Y. Srinivas, K. Sunil Babu, V. Sunndadara Siva Kumar and A. Hanumaiah

(Continued on the Bookbinding Inside Back Cover) 090305 Spin and pseudospin symmetric Dirac particles in the field of Tietz Hua potential including Coulomb tensor interaction Sameer M. Ikhdair and Majid Hamzavi 090306 Generalized quantum mechanical two-Coulomb-center problem (Demkov problem) A. M. Puchkov, A. V. Kozedub and E. O. Bodnia 090307 Comparison of entanglement trapping among different photonic band gap models Zhang Ying-Jie, Yang Xiu-Qin, Han Wei and Xia Yun-Jie 090308 Topological properties of one-dimensional hardcore Bose–Fermi mixture Jia Yong-Fei, Guo Huai-Ming, Qin Ji-Hong, Chen Zi-Yu and Feng Shi-Ping 090309 Complete four-photon cluster-state analyzer based on cross-Kerr nonlinearity Wang Zhi-Hui, Zhu Long, Su Shi-Lei, Guo Qi, Cheng Liu-Yong, Zhu Ai-Dong and Zhang Shou 090310 Accelerating an adiabatic process by nonlinear sweeping Cao Xing-Xin, Zhuang Jun, Ning Xi-Jing and Zhang Wen-Xian 090311 Distributed wireless quantum communication networks Yu Xu-Tao, Xu Jin and Zhang Zai-Chen 090312 Spectroscopy and coherent manipulation of single and coupled flux qubits Wu Yu-Lin, Deng Hui, Huang Ke-Qiang, Tian Ye, Yu Hai-Feng, Xue Guang-Ming, Jin Yi-Rong, Li Jie, Zhao Shi-Ping and Zheng Dong-Ning 090313 The effects of the Dzyaloshinskii–Moriya interaction on the ground-state properties of the XY chain in a transverse field Zhong Ming, Xu Hui, Liu Xiao-Xian and Tong Pei-Qing 090314 Effects of three-body interaction on dynamic and static structure factors of an optically-trapped Bose gas Qi Wei, Liang Zhao-Xin and Zhang Zhi-Dong 090501 Particle–hole bound states of dipolar molecules in an optical lattice Zhang Yi-Cai, Wang Han-Ting, Shen Shun-Qing and Liu Wu-Ming 090502 Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof Song Rui-Zhuo, Xiao Wen-Dong, Sun Chang-Yin and Wei Qing-Lai 090503 Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems Feng Jing-Jing, Zhang Qi-Chang, Wang Wei and Hao Shu-Ying 090504 Cluster exponential synchronization of a class of complex networks with hybrid coupling and time- varying delay Wang Jun-Yi, Zhang Hua-Guang, Wang Zhan-Shan and Liang Hong-Jing 090505 Nonautonomous deformed solitons in a Bose–Einstein condensate Li Ze-Jun, Hai Wen-Hua and Deng Yan 090601 Clock-transition spectrum of 171Yb atoms in a one-dimensional optical lattice Chen Ning, Zhou Min, Chen Hai-Qin, Fang Su, Huang Liang-Yu, Zhang Xiao-Hang, Gao Qi, Jiang Yan-Yi, Bi Zhi-Yi, Ma Long-Sheng and Xu Xin-Ye

(Continued on the Bookbinding Inside Back Cover) 090701 A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method Zhang Chen, Shou Guo-Fa, Lu Hong, Hua Ning, Tang Xue-Zheng, Xia Ling, Ma Ping and Tang Fa-Kuan

ATOMIC AND MOLECULAR PHYSICS

+ 093101 Vibrational transition spectra of H2 in a strong magnetic ﬁeld Hu Shi-Lin and Shi Ting-Yun 093102 Multireference conﬁguration interaction study on spectroscopic properties of low-lying electronic states

of As2 molecule Wang Jie-Min and Liu Qiang 093201 Significant discrepancy between the ionization time for parallel and anti-parallel electron emission in sequential double ionization Wang Xiao-Shan, Du Hong-Chuan, Luo Lao-Yong and Hu Bi-Tao 093202 Method of accurately calculating mean field operator in multi-configuration time-dependent Hartree– Fock frame Li Wen-Liang, Zhang Ji and Yao Hong-Bin + 093301 High resolution photoassociation spectra of an ultracold Cs2 long-range 0u (6S1/2 + 6P1/2) state Chen Peng, Li Yu-Qing, Zhang Yi-Chi, Wu Ji-Zhou, Ma Jie, Xiao Lian-Tuan and Jia Suo-Tang − 093701 Photoassociation of ultracold RbCs molecules into the (2)0 state (v = 189,190) below the 5S1/2 + 6P1/2 dissociation limit Chang Xue-Fang, Ji Zhong-Hua, Yuan Jin-Peng, Zhao Yan-Ting, Yang Yong-Gang, Xiao Lian-Tuan and Jia Suo-Tang

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

094101 A double constrained robust capon beamforming based imaging method for early breast cancer detection Xiao Xia, Xu Li and Li Qin-Wei 094102 Tunability of graded negative index-based photonic crystal lenses for ﬁne focusing Jin Lei, Zhu Qing-Yi and Fu Yong-Qi 094103 Varactor-tunable frequency selective surface with an embedded bias network Lin Bao-Qin, Qu Shao-Bo, Tong Chuang-Ming, Zhou Hang, Zhang Heng-Yang and Li Wei

2+ 3+ 094201 Inﬂuences of Mg ion on dopant occupancy and upconversion luminescence of Ho ion in LiNbO3 crystal Dai Li, Xu Chao, Zhang Ying, Li Da-Yong and Xu Yu-Heng 094202 An image joint compression-encryption algorithm based on adaptive arithmetic coding Deng Jia-Xian and Deng Hai-Tao 094203 Analytical approach to dynamics of transformed rotating-wave approximation with dephasing M. Mirzaee and N. Kamani

(Continued on the Bookbinding Inside Back Cover) 094204 Measurement of intensity difference squeezing via non-degenerate four-wave mixing process in an atomic vapor Yu Xu-Dong, Meng Zeng-Ming and Zhang Jing 094205 Coherent effect of triple-resonant optical parametric amplification inside a cavity with injection of a squeezed vacuum field Di Ke and Zhang Jing 094206 Generation of a continuous-wave squeezed vacuum state at 1.3 µm by employing a home-made all-solid- state laser as pump source Zheng Yao-Hui, Wu Zhi-Qiang, Huo Mei-Ru and Zhou Hai-Jun 094207 Spontaneous emission of two quantum dots in a single-mode cavity Qiu Liu, Zhang Ke and Li Zhi-Yuan 094208 High power 2-µm room-temperature continuous-wave operation of GaSb-based strained quantum-well lasers Xu Yun, Wang Yong-Bin, Zhang Yu, Song Guo-Feng and Chen Liang-Hui 094210 Reflective graphene oxide absorber for passively mode-locked laser operating at nearly 1 µm Yang Ji-Min, Yang Qi, Liu Jie, Wang Yong-Gang and Yuen H. Tsang 094211 A grating-coupled external cavity InAs/InP quantum dot laser with 85-nm tuning range Wei Heng, Jin Peng, Luo Shuai, Ji Hai-Ming, Yang Tao, Li Xin-Kun, Wu Jian, An Qi, Wu Yan-Hua, Chen Hong-Mei, Wang Fei-Fei, Wu Ju and Wang Zhan-Guo 094212 Shaping of few-cycle laser pulses via a subwavelength structure Guo Liang, Xie Xiao-Tao and Zhan Zhi-Ming 094213 Effects of clouds, sea surface temperature, and its diurnal variation on precipitation efficiency Shen Xin-Yong, Qing Tao and Li Xiao-Fan 094214 An all-silicone zoom lens in an optical imaging system Zhao Cun-Hua 094215 All-optical modulator based on a ferrofluid core metal cladding waveguide chip Han Qing-Bang, Yin Cheng, Li Jian, Tang Yi-Bin, Shan Ming-Lei and Cao Zhuang-Qi 094601 Block basis property of a class of 2 × 2 operator matrices and its application to elasticity Song Kuan, Hou Guo-Lin and Alatancang 094701 Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity Ahmed M. Megahed

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

095201 Simulation of electron cyclotron current drive and electron cyclotron resonant heating for the HL-2A tokamak Wang Zhong-Tian, Long Yong-Xing, Dong Jia-Qi and He Zhi-Xiong

(Continued on the Bookbinding Inside Back Cover) CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

096101 Mechanical behavior of Cu–Zr bulk metallic glasses (BMGs): A molecular dynamics approach Muhammad Imran, Fayyaz Hussain, Muhammad Rashid, Yongqing Cai and S. A. Ahmad 096102 Interaction of point defects with twin boundaries in Au: A molecular dynamics study Fayyaz Hussain, Sardar Sikandar Hayat, Zulﬁqar Ali Shah, Najmul Hassan and Shaikh Aftab Ahmad 096103 Large energy-loss straggling of swift heavy ions in ultra-thin active silicon layers Zhang Zhan-Gang, Liu Jie, Hou Ming-Dong, Sun You-Mei, Zhao Fa-Zhan, Liu Gang, Han Zheng-Sheng, Geng Chao, Liu Jian-De, Xi Kai, Duan Jing-Lai, Yao Hui-Jun, Mo Dan, Luo Jie, Gu Song and Liu Tian-Qi 096201 The application of reed-vibration mechanical spectroscopy for liquids to detect chemical reactions of an acrylic structural adhesive Wei Lai, Zhou Heng-Wei, Zhang Li and Huang Yi-Neng

096202 In situ electrical resistance and activation energy of solid C60 under high pressure Yang Jie, Liu Cai-Long and Gao Chun-Xiao 096301 High-pressure phonon dispersion of copper by using the modiﬁed analytic embedded atom method Zhang Xiao-Jun, Chen Chang-Le and Feng Fei-Long 096401 Copolymer homopolymer mixtures in a nanopore Zhang Ling-Cui, Sun Min-Na, Pan Jun-Xing, Wang Bao-Feng, Zhang Jin-Jun and Wu Hai-Shun 096701 Effects of transverse trapping on the ground state of a cigar-shaped two-component Bose Einstein condensate Cui Guo-Dong, Sun Jian-Fang, Jiang Bo-Nan, Qian Jun and Wang Yu-Zhu 096702 Extended Bose Hubbard model with pair hopping on triangular lattice Wang Yan-Cheng, Zhang Wan-Zhou, Shao Hui and Guo Wen-An 096802 Evolution behavior of catalytically activated replication decline in a coagulation process Gao Yan, Wang Hai-Feng, Zhang Ji-Dong, Yang Xia, Sun Mao-Zhu and Lin Zhen-Quan

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTI- CAL PROPERTIES 097101 Modeling of conducting bridge evolution in bipolar vanadium oxide-based resistive switching memory Zhang Kai-Liang, Liu Kai, Wang Fang, Yin Fu-Hong, Wei Xiao-Ying and Zhao Jin-Shi 097201 A novel 4H-SiC lateral bipolar junction transistor structure with high voltage and high current gain Deng Yong-Hui, Xie Gang, Wang Tao and Sheng Kuang

097301 Improved interface properties of an HfO2 gate dielectric GaAs MOS device by using SiNx as an interfa- cial passivation layer Zhu Shu-Yan, Xu Jing-Ping, Wang Li-Sheng and Huang Yuan 097302 High-performance 4H-SiC junction barrier Schottky diodes with double resistive termination extensions Zheng Liu, Zhang Feng, Liu Sheng-Bei, Dong Lin, Liu Xing-Fang, Fan Zhong-Chao, Liu Bin, Yan Guo-Guo, Wang Lei, Zhao Wan-Shun, Sun Guo-Sheng, He Zhi and Yang Fu-Hua

(Continued on the Bookbinding Inside Back Cover) 097303 Field plate structural optimization for enhancing the power gain of GaN-based HEMTs Zhang Kai, Cao Meng-Yi, Lei Xiao-Yi, Zhao Sheng-Lei, Yang Li-Yuan, Zheng Xue-Feng, Ma Xiao-Hua and Hao Yue 097304 Effect of optical pumping on the momentum relaxation time of graphene in the terahertz range Zuo Zhi-Gao, Wang Ping, Ling Fu-Ri, Liu Jin-Song and Yao Jian-Quan 097401 Fabrication of rhenium Josephson junctions Xue Guang-Ming, Yu Hai-Feng, Tian Ye, Liu Wei-Yang, Yu Hong-Wei, Ren Yu-Feng and Zhao Shi-Ping 097502 Preparation of gold tetrananocages and their photothermal effect Yin Nai-Qiang, Liu Ling, Lei Jie-Mei, Jiang Tong-Tong, Zhu Li-Xin and Xu Xiao-Liang 097701 Performance improvement of charge trap ﬂash memory by using a composition-modulated high-k trapping layer Tang Zhen-Jie, Li Rong and Yin Jiang

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 098101 Crystallization of polymer chains induced by graphene: Molecular dynamics study Yang Jun-Sheng, Huang Duo-Hui, Cao Qi-Long, Li Qiang, Wang Li-Zhi and Wang Fan-Hou 098102 Germanium nanoislands grown by radio frequency magnetron sputtering: Annealing time dependent surface morphology and photoluminescence Alireza Samavati, Z. Othaman, S. K. Ghoshal and R. J. Amjad 098103 Structural and optical properties of a NaCl single crystal doped with CuO nanocrystals S. Addala, L. Bouhdjer, A. Chala, A. Bouhdjar, O. Halimi, B. Boudine and M. Sebais 098104 Interface evolution of a particle in a supersaturated solution affected by a far-field uniform flow Chen Ming-Wen and Wang Zi-Dong 098401 Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode Zhang Wei-Ya, Li Yong-Li, Chang Xiao-Yong and Wang Nan 098501 Effect of ionizing radiation on dual 8-bit analog-to-digital converters (AD9058) with various dose rates and bias conditions Li Xing-Ji, Liu Chao-Ming, Sun Zhong-Liang, Xiao Li-Yi and He Shi-Yu 098502 Tight-binding study of quantum transport in nanoscale GaAs Schottky MOSFET Zahra Ahangari and Morteza Fathipour

098503 Characterization and luminescence of Eu/Sm-coactivated CaYAl3O7 phosphor synthesized by using a combustion method Yu Hong-Ling, Yu Xue, Xu Xu-Hui, Jiang Ting-Ming, Yang Peng-Hui, Jiao Qing, Zhou Da-Cheng and Qiu Jian-Bei

(Continued on the Bookbinding Inside Back Cover) 098504 Efficiency and droop improvement in a blue InGaN-based light emitting diode with a p-InGaN layer inserted in the GaN barriers Wang Xing-Fu, Tong Jin-Hui, Zhao Bi-Jun, Chen Xin, Ren Zhi-Wei, Li Dan-Wei, Zhuo Xiang-Jing, Zhang Jun, Yi Han-Xiang and Li Shu-Ti 098701 Processes of DNA condensation induced by multivalent cations: Approximate annealing experiments and molecular dynamics simulations Chai Ai-Hua, Ran Shi-Yong, Zhang Dong, Jiang Yang-Wei, Yang Guang-Can and Zhang Lin-Xi 098702 Online multiple instance regression Wang Zhi-Gang, Zhao Zeng-Shun and Zhang Chang-Shui 098703 Characterizing neural activities evoked by manual acupuncture through spiking irregularity measures Xue Ming, Wang Jiang, Deng Bin, Wei Xi-Le, Yu Hai-Tao and Chen Ying-Yuan 098801 Dependence of InGaN solar cell performance on polarization-induced electric field and carrier lifetime Yang Jing, Zhao De-Gang, Jiang De-Sheng, Liu Zong-Shun, Chen Ping, Li Liang, Wu Liang-Liang, Le Ling- Cong, Li Xiao-Jing, He Xiao-Guang, Wang Hui, Zhu Jian-Jun, Zhang Shu-Ming, Zhang Bao-Shun and Yang Hui 098802 Electron beam evaporation deposition of cadmium sulphide and cadmium telluride thin films: Solar cell applications Fang Li, Chen Jing, Xu Ling, Su Wei-Ning, Yu Yao, Xu Jun and Ma Zhong-Yuan

098803 Numerical simulation of a triple-junction thin-ﬁlm solar cell based on µc-Si1−xGex:H Huang Zhen-Hua, Zhang Jian-Jun, Ni Jian, Cao Yu, Hu Zi-Yang, Li Chao, Geng Xin-Hua and Zhao Yin

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

85 099501 Dependence of the Rb coherent population trapping resonance characteristic on the pressure of N2 buffer gas Qu Su-Ping, Zhang Yi and Gu Si-Hong