Dynamical correlation functions of the quadratic coupling spin-Boson model

doi:10.1088/1674-1056/26/6/060502

Abstract

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions C_O(ω), with the operator Ô taken as σ_x, σ_z, and X, respectively. In the weak-coupling regime α < α_c, these functions show power law ω-dependence in the small frequency limit, with the powers 1+2s, 1+2s, and s, respectively. At the critical point α=α_c of the boson-unstable quantum phase transition, the critical exponents y_O of these correlation functions are obtained as y_{σ_x}=y_{σ_z}=1-2s and y_X=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of C_{σ_x}(ω) is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Keywords: quadratic-coupling spin-boson model numerical renormalization group quantum phase transition dynamical correlation function

Received: 20 February 2017
Revised: 21 March 2017
Accepted manuscript online:

PACS:	05.10.Cc	(Renormalization group methods)
	64.70.Tg	(Quantum phase transitions)
	03.65.Yz	(Decoherence; open systems; quantum statistical methods)
	05.30.Jp	(Boson systems)

Fund:

Project supported by the National Key Basic Research Program of China (Grant No. 2012CB921704), the National Natural Science Foundation of China (Grant No. 11374362), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 15XNLQ03).

Corresponding Authors: Ning-Hua Tong
E-mail: nhtong@ruc.edu.cn

Cite this article:

Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华) Dynamical correlation functions of the quadratic coupling spin-Boson model 2017 Chin. Phys. B 26 060502

[1]	Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W 59 1
[2]	Weiss U 1993 Quantum Dissipative Systems (Singapore: World Scientific)
[3]	Caldeira A O and Leggett A J 1983 Ann. Phys. 149 374
[4]	Kehrein S and Mielke A 219 313
[5]	Bulla R, Tong N H and Vojta M 91 170601
[6]	Bulla R, Lee H J, Tong N H and Vojta M 2005 Phys. Rev. B 71 045122
[7]	Zhao C J, Lü Z G and Zheng H 2011 Phys. Rev. E 80 011114
[8]	Zheng H and Lü Z G 2013 J. Chem. Phys. 138 174117
[9]	Vojta M 2006 Phil. Mag. 86 1807
[10]	Vojta M, Tong N H and Bulla R 94 070604
[11]	Vojta M, Tong N H and Bulla R 102 249904(E)
[12]	Vojta M, Bulla R, Güttge F and Anders F 81 075122
[13]	Winter A, Rieger H, Vojta M and Bulla R 2009 Phys. Rev. Lett. 102 030601
[14]	Alvermann A and Fehske H 2009 Phys. Rev. Lett. 102 150601
[15]	Guo C, Weichselbaum A, von Delft J and Vojta M 2012 Phys. Rev. Lett. 108 160401
[16]	Hou Y H and Tong T H 78 127
[17]	Tong N H and Hou Y H 2012 Phys. Rev. B 85 144425
[18]	Recati A, Fedichev P O, Zwerger W, von Delft J and Zoller P 94 040404
[19]	Tong N H and Vojta M 97 016802
[20]	Yu L B, Tong N H, Xue Z Y, Wang Z D and Zhu S L 55 1557
[21]	Orth P P, Stanic I and Le Hur K 77 051601(R)
[22]	Porras D, Marquardt F, von Delft J and Cirac J I 78 010101(R)
[23]	Vion D, Aassime A, Cottet A, Joyez P, Pothier H, Urbina C, Esteve D and Devoret M H 296 886
[24]	Bertet P, Chiorescu I, Burkard G, Semba K, Harmans C J P M, DiVincenzo D P and Mooij J E 95 257002
[25]	Ithier G, Collin E, Joyez P, Meeson P J, Vion D, Esteve D, Chiarello F, Shnirman A, Makhlin Y, Schriefl J and Schön G 2005 Phys. Rev. B 72 134519
[26]	Yoshihara F, Harrabi K, Niskanen A O, Nakamura Y and Tsai J S 97 167001
[27]	Kakuyanagi K, Meno T, Saito S, Nakano H, Semba K, Takayanagi H, Deppe F and Shnirman A 98 047004
[28]	Makhlin Y and Shnirman A 92 178301
[29]	Bergli J, Galperin Y M and Altshuler B L 74 024509
[30]	Cywiński L 90 042307
[31]	Balian S J, Liu R B and Monteiro T S 91 245416
[32]	Muljarov E A and Zimmermann R 93 237401
[33]	Borri P, Langbein W, Schneider S, Woggon U, Sellin R L, Ouyang D and Bimberg D 87 157401
[34]	Maghrebi M F, Krüger M and Kardar M 93 014309
[35]	Zheng D C and Tong N H 2016 arXiv: 1612.09437v1 [cond-mat.mes-hall]
[36]	Wilson K G 1975 Rev. Mod. Phys. 47 773
[37]	Bulla R, Costi T A and Pruschke T 2008 Rev. Mod. Phys. 80 395
[38]	Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hümmer T, Solano E, Marx A and Gross R 6 772
[39]	Forn-Díaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M and Mooij J E 2010 Phys. Rev. Lett. 105 237001
[40]	Bulla R, Costi T A and Vollhardt D 2001 Phys. Rev. B 64 045103
[41]	Peters R, Pruschke T and Anders F J 74 245114
[42]	Weichselbaum A and von Delft J 99 076402
[43]	Yoshida M, Whitaker M A and Oliveira L N 41 9403
[44]	Oliveira W C and Oliveira L N \textbf 49 11986
[45]	Bulla R, Hewson A C and Pruschke T 10 8365
[46]	Campo V L and Oliveira L N 72 104432
[47]	Žitko R and Pruschke T 79 085106
[48]	Žitko R 84 085142
[49]	Freyn A and Florens S 79 121102(R)
[50]	Osolin Ž and Žitko R 87 245135
[51]	Lü Z G and Zheng H 2007 Phys. Rev. B 75 054302

[1]	Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Chin. Phys. B, 2022, 31(7): 070502.
[2]	Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆). Chin. Phys. B, 2022, 31(6): 060505.
[3]	A sport and a pastime: Model design and computation in quantum many-body systems Gaopei Pan(潘高培), Weilun Jiang(姜伟伦), and Zi Yang Meng(孟子杨). Chin. Phys. B, 2022, 31(12): 127101.
[4]	Quantum phase transitions in CePdAl probed by ultrasonic and thermoelectric measurements Hengcan Zhao(赵恒灿), Meng Lyu(吕孟), Jiahao Zhang(张佳浩), Shuai Zhang(张帅), and Peijie Sun(孙培杰). Chin. Phys. B, 2022, 31(11): 117103.
[5]	Ferromagnetic Heisenberg spin chain in a resonator Yusong Cao(曹雨松), Junpeng Cao(曹俊鹏), and Heng Fan(范桁). Chin. Phys. B, 2021, 30(9): 090506.
[6]	Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[7]	Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Chin. Phys. B, 2021, 30(6): 067505.
[8]	Quantum simulations with nuclear magnetic resonance system Chudan Qiu(邱楚丹), Xinfang Nie(聂新芳), and Dawei Lu(鲁大为). Chin. Phys. B, 2021, 30(4): 048201.
[9]	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.
[10]	Classical-field description of Bose-Einstein condensation of parallel light in a nonlinear optical cavity Hui-Fang Wang(王慧芳), Jin-Jun Zhang(张进军), and Jian-Jun Zhang(张建军). Chin. Phys. B, 2021, 30(11): 110301.
[11]	Tunable deconfined quantum criticality and interplay of different valence-bond solid phases Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[12]	Dissipative quantum phase transition in a biased Tavis-Cummings model Zhen Chen(陈臻), Yueyin Qiu(邱岳寅), Guo-Qiang Zhang(张国强), Jian-Qiang You(游建强). Chin. Phys. B, 2020, 29(4): 044201.
[13]	Controllable precision of the projective truncation approximation for Green's functions Peng Fan(范鹏), Ning-Hua Tong(同宁华). Chin. Phys. B, 2019, 28(4): 047102.
[14]	Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime Ji-Li Liu(刘吉利), Jiu-Qing Liang(梁九卿). Chin. Phys. B, 2019, 28(11): 110304.
[15]	Heavy fermions in high magnetic fields M Smidman, B Shen(沈斌), C Y Guo(郭春煜), L Jiao(焦琳), X Lu(路欣), H Q Yuan(袁辉球). Chin. Phys. B, 2019, 28(1): 017106.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamical correlation functions of the quadratic coupling spin-Boson model

Cite this article:

Online attention