Dynamics of one-dimensional random quantum XY system with Dzyaloshinskii–Moriya interaction

doi:10.1088/1674-1056/22/3/037502

Abstract In this paper, the effects of random variables on the dynamics of the s=1/2 XY model with the Dzyaloshinskii–Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δ_j (or the standard deviation of random external field δ_B) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δ_J (or δ_B) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.

Keywords: correlation function spectral density Dzyaloshinskii–Moriya interaction recurrence relation method

Received: 22 June 2012
Revised: 26 September 2012
Accepted manuscript online:

PACS:	75.10.Pq	(Spin chain models)
	75.10.Jm	(Quantized spin models, including quantum spin frustration)
	75.40.Gb	(Dynamic properties?)
	75.50.Lk	(Spin glasses and other random magnets)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10775088), the Shandong Natural Science Foundation, China (Grant No. Y2006A05), and the Science Foundation of Qufu Normal University, China.

Corresponding Authors: Kong Xiang-Mu
E-mail: kongxm@mail.qfnu.edu.cn

Cite this article:

Li Yin-Fang (李银芳), Kong Xiang-Mu (孔祥木) Dynamics of one-dimensional random quantum XY system with Dzyaloshinskii–Moriya interaction 2013 Chin. Phys. B 22 037502

[1]	Honarasa G R, Tavassoly M K and Hatami M 2012 Chin. Phys. B 21 054208
[2]	Florencio J and Sá Barreto F C 1999 Phys. Rev. B 60 9555
[3]	Boechat B, Cordeiro C, Florencio J, Sá Barreto F C and de Alcantara Bonfim O F 2000 Phys. Rev. B 61 14327
[4]	Basak R and Chatterjee I 1989 Phys. Rev. B \bf40 4627
[5]	Goovaerts E, De Raedt H and Schoemaker D 1984 Phys. Rev. Lett. 52 1649
[6]	Lieb E, Schultz T D and Mattis D C 1961 Ann. Phys. 16 407
[7]	Florencio J and Lee M H 1987 Phys. Rev. B 35 1835
[8]	Niemeijer T 1967 Physica 36 377
[9]	McCoy B M 1968 Phys. Rev. 173 531
[10]	Barouch E and McCoy B M 1971 Phys. Rev. A 3 786
[11]	Plascak J A, Pires A S T and Sá Barreto F C 1982 Solid State Commun. 44 787
[12]	Plascak J A, Sá Barreto F C, Pires A S T and Goncalves L L 1983 J. Phys. C 16 49
[13]	Watarai S and Matsubara T 1984 J. Phys. Soc. Jpn. 53 3648
[14]	Levitsky R R, Grigas J, Zachek I R, Mits Y V and Paprotny W 1986 Ferroelectrics 67 109
[15]	Wu W, Ellman B, Rosenbaum T F, Aeppli G and Reich D H 1991 Phys. Rev. Lett. 67 2076
[16]	Nunes M E S and Florencio J 2003 Phys. Rev. B 68 014406
[17]	Yuan X J, Zhao B Y, Chen S X and Kong X M 2010 Acta Phys. Sin. 59 1499 (in Chinese)
[18]	Li Y F, Shen Y Y and Kong X M 2012 Acta Phys. Sin. 61 107501 (in Chinese)
[19]	Boechat B, Cordeiro C, de Alcantara Bonfim O F, Florencio J and Sá Barreto F C 2000 Braz. J. Phys. 30 693
[20]	de Alcantara Bonfim O F, Boechat B, Cordeiro C, Sá Barreto F C and Florencio J 2001 J. Phys. Soc. Jpn. 70 829
[21]	Jafari R, Kargarian M, Langari A and Siahatgar M 2008 Phys. Rev. B 78 214414
[22]	Kargarian M, Jafari R and Langari A 2009 Phys. Rev. A 79 042319
[23]	Zhang X P, Ren Z Z, Zheng Q and Zhi Q J 2009 Chin. Phys. B 18 3210
[24]	Viswanath V S and Müller G, 1994 The Recursion Method-Applications to Many-Body Dynamics (Berlin: Springer)
[25]	Mori H 1965 Prog. Theor. Phys. 34 399
[26]	Lee M H 1982 Phys. Rev. Lett. 49 1072
[27]	Lee M H 1982 Phys. Rev. B 26 2547
[28]	Lee M H 1983 J. Math. Phys. 24 2512
[29]	Lee M H, Hong J and Florencio J 1987 Phys. Scr. 1987 498
[30]	Stolze J, Viswanath V S and Müller G 1992 Z. Phys. B 89 45
[31]	Xu Z B, Kong X M and Liu Z Q 2008 Phys. Rev. B 77 184414
[32]	Schotte U, Hoser A and Stüβ er N 2000 Solid State Commun. 113 523
[33]	Zhao J Z, Wang X Q, Xiang T, Su Z B and Yu L 2003 Phys. Rev. Lett. 90 207204
[34]	Kavokin K V 2001 Phys. Rev. B 64 075305
[35]	Kavokin K V 2004 Phys.Rev. B 69 075302

[1]	Equilibrium dynamics of the sub-ohmic spin-boson model at finite temperature Ke Yang(杨珂) and Ning-Hua Tong(同宁华). Chin. Phys. B, 2021, 30(4): 040501.
[2]	Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas EJKP Nandani, Xi-Wen Guan(管习文). Chin. Phys. B, 2018, 27(7): 070306.
[3]	Ghost images reconstructed from fractional-order moments with thermal light De-Zhong Cao(曹德忠), Qing-Chen Li(李清晨), Xu-Cai Zhuang(庄绪财), Cheng Ren(任承), Su-Heng Zhang(张素恒), Xin-Bing Song(宋新兵). Chin. Phys. B, 2018, 27(12): 123401.
[4]	Dynamical correlation functions of the quadratic coupling spin-Boson model Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华). Chin. Phys. B, 2017, 26(6): 060502.
[5]	Equilibrium dynamics of the sub-Ohmic spin-boson model under bias Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华). Chin. Phys. B, 2017, 26(6): 060501.
[6]	Photon statistics of pulse-pumped four-wave mixing in fiber with weak signal injection Nan-Nan Liu(刘楠楠), Yu-Hong Liu(刘宇宏), Jia-Min Li(李嘉敏), Xiao-Ying Li(李小英). Chin. Phys. B, 2016, 25(7): 074203.
[7]	The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder Liu Zhong-Qiang (刘中强), Jiang Su-Rong (姜素蓉), Kong Xiang-Mu (孔祥木). Chin. Phys. B, 2014, 23(8): 087505.
[8]	Thermodynamic properties of Heisenberg magnetic systems Qin Wei (秦伟), Wang Huai-Yu (王怀玉), Long Gui-Lu (龙桂鲁). Chin. Phys. B, 2014, 23(3): 037502.
[9]	A robust power spectrum split cancellation-based spectrum sensing method for cognitive radio systems Qi Pei-Han (齐佩汉), Li Zan (李赞), Si Jiang-Bo (司江勃), Gao Rui (高锐). Chin. Phys. B, 2014, 23(12): 128401.
[10]	Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on the square lattice M Y Ali, J Poulter. Chin. Phys. B, 2013, 22(6): 067502.
[11]	Ballistic diffusion induced by non-Gaussian noise Qin Li (覃莉), Li Qiang (李强). Chin. Phys. B, 2013, 22(3): 038701.
[12]	Quantum correlation dynamics of three non-coupled two-level atoms in different reservoirs Wang Xiao-Yun (王小云), Ding Bang-Fu (丁邦福), Zhao He-Ping (赵鹤平). Chin. Phys. B, 2013, 22(2): 020309.
[13]	A comparative study on geometries, stabilities, and electronic properties between bimetallic Ag_nX (X=Au, Cu; n=1-8) and pure silver clusters Ding Li-Ping(丁利苹), Kuang Xiao-Yu(邝小渝), Shao Peng(邵鹏), Zhao Ya-Ru(赵亚儒), and Li Yan-Fang(李艳芳) . Chin. Phys. B, 2012, 21(4): 043601.
[14]	Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation Ding Bang-Fu (丁邦福), Wang Xiao-Yun (王小云), Tang Yan-Fang (唐艳芳), Mi Xian-Wu (米贤武), Zhao He-Ping (赵鹤平). Chin. Phys. B, 2011, 20(6): 060304.
[15]	Scaling of entanglement entropy for spin chain with Dzyaloshinskii–Moriya interaction Du Long(杜龙),Hou Jing-Min(侯净敏),Ding Jia-Yan(丁伽焱), Zhang Wen-Xin(张文新),Tian Zhi(田志),and Chen Ting-Ting(陈婷婷) . Chin. Phys. B, 2011, 20(2): 020306.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamics of one-dimensional random quantum XY system with Dzyaloshinskii–Moriya interaction

Cite this article:

Online attention