Controllable precision of the projective truncation approximation for Green's functions

doi:10.1088/1674-1056/28/4/047102

Abstract

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions (Fan et al., Phys. Rev. B 97, 165140 (2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.

Keywords: projective truncation approximation two-time Green' s functions single-band Anderson impurity model numerical renormalization group

Received: 16 December 2018
Revised: 18 February 2019
Accepted manuscript online:

PACS:	71.20.Be	(Transition metals and alloys)
	71.10.Fd	(Lattice fermion models (Hubbard model, etc.))
	24.10.Cn	(Many-body theory)

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, 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:

Peng Fan(范鹏), Ning-Hua Tong(同宁华) Controllable precision of the projective truncation approximation for Green's functions 2019 Chin. Phys. B 28 047102

[1]	Martin P C and Schwinger J 1959 Phys. Rev. 115 1342
[2]	Bogolyubov N and Tyablikov S V 1959 Doklady. Akad. Nauk SSSR 126 53
[3]	Tyablikov S V, 1959 Vkrain. Mat. Zhur. 11 287
[4]	Zubarev D N 1960 Usp. Fiz. Nauk 71 71
[5]	Mori H 1965 Prog. Theor. Phys. 33 423
[6]	Mori H 1965 Prog. Theor. Phys. 34 399
[7]	Zwanzig R 1961 Lectures in Theoretical Physics, Vol. 3 (New York: Interscience)
[8]	Lee M H 1982 Phys. Rev. Lett. 49 1072
[9]	Lee M H 2000 Phys. Rev. E 62 1769
[10]	Tserkovnikov Yu A 1981 Theor. Math. Phys. 49 993
[11]	Tserkovnikov Yu A 1999 Theor. Math. Phys. 118 85
[12]	Roth L M 1968 Phys. Rev. Lett. 20 1431
[13]	Roth L M 1969 Phys. Rev. 184 451
[14]	Mancini F and Avella A 2004 Adv. Phys. 53 537
[15]	Avella A 2014 Adv. Conden. Matter Phys. 2014 515698
[16]	Kakehashi Y and Fulde P 2004 Phys. Rev. B 70 195102
[17]	Fulde P 1995 Electron Correlations in Molecules and Solids, 3rd edn. (Berlin, Heidelberg, New York: Springer-Verlag)
[18]	Onoda S and Imdada M 2001 J. Phys. Soc. Jpn. 70 632
[19]	Onoda S and Imdada M 2001 J. Phys. Soc. Jpn. 70 3398
[20]	Onoda S and Imada M 2003 Phys. Rev. B 67 161102(R)
[21]	Kuzemsky A L 2002 Rivista Nuovo Cimento 25 1
[22]	Rowe D J 1968 Rev. Mod. Phys. 40 153
[23]	Plakida N M 2012 “Strongly Correlated Systems” ed. Avella A and Mancini F, Springer Series in Solid-State Sciences, Vol. 171 (Berlin, Heidelberg: Springer)
[24]	Lee M H, Hong J, and Florencio J 1987 Phys. Scr. T19 498
[25]	Fan P, Yang K, Ma K H and Tong N H 2018 Phys. Rev. B 97 165140
[26]	Lacroix C 1981 J. Phys. F: Metal Phys. 11 2389
[27]	Wilson K G 1975 Rev. Mod. Phys. 47 773
[28]	Hubbard J 1963 Proc. Roy. Soc. London Ser. A 276 238
[29]	Hubbard J 1963 Proc. Roy. Soc. London Ser. A 277 237
[30]	Hubbard J 1964 Proc. Roy. Soc. London Ser. A 281 401
[31]	Sindel M, Borda L, Martinek J, Bulla R, König J, Schön G, Maekawa S and von Delft J 2007 Phys. Rev. B 76 045321
[32]	Metzner W and Vollhardt D 1989 Phys. Rev. Lett. 62 324
[33]	Georges A, Kotliar G, Krauth W and Rozenberg M J 1996 Rev. Mod. Phys. 68 13
[34]	Gebhard F 1997 The Mott Metal-Insulator Transition (Berlin, Heidelberg, New York: Springer-Verlag)
[35]	Ma K H and Tong N H arXiv: 1901.11471 (unpublished)
[36]	Weichselbaum A and von Delft J 2007 Phys. Rev. Lett. 99 076402
[37]	Peters R, Pruschke T and Anders F B 2006 Phys. Rev. B 74 245114
[38]	Bulla R, Hewson A C and Pruschke Th 1998 J. Phys.: Condens. Matter 10 8365
[39]	Yoshida M, Whitaker M A and Oliveira L N 1990 Phys. Rev. B 41 9403
[40]	The convergence of the NRG result for LDOS of AIM with respect to L and Ms was discussed in Supplementary Materials of Li Z H et al. 2012 Phys. Rev. Lett. 109 266403
[41]	Ciolo A D and Avella A 2018 Physica B 536 687
[42]	Tong N H 2015 Phys. Rev. B 92 165126

[1]	Device design based on the covalent homocouplingof porphine molecules Minghui Qu(曲明慧), Jiayi He(贺家怡), Kexin Liu(刘可心), Liemao Cao(曹烈茂), Yipeng Zhao(赵宜鹏), Jing Zeng(曾晶), and Guanghui Zhou(周光辉). Chin. Phys. B, 2021, 30(9): 098504.
[2]	Exploring how hydrogen at gold-sulfur interface affects spin transport in single-molecule junction Jing Zeng(曾晶), Ke-Qiu Chen(陈克求), Yanhong Zhou(周艳红). Chin. Phys. B, 2020, 29(8): 088503.
[3]	Designing of spin filter devices based on zigzag zinc oxide nanoribbon modified by edge defect Bao-Rui Huang(黄保瑞), Fu-Chun Zhang(张富春), Yan-Ning Yang(杨延宁), Zhi-Yong Zhang(张志勇), Wei-Guo Wang(王卫国). Chin. Phys. B, 2019, 28(10): 108503.
[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]	Kosterlitz-Thouless transition, spectral property and magnetic moment for a two-dot structure with level difference Yong-Chen Xiong(熊永臣), Wang-Huai Zhou(周望怀), Jun Zhang(张俊), Nan Nan(南楠). Chin. Phys. B, 2017, 26(6): 067501.
[6]	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.
[7]	The construction of general basis functions in reweighting ensemble dynamics simulations: Reproduce equilibrium distribution in complex systems from multiple short simulation trajectories Zhang Chuan-Biao (张传彪), Li Ming (黎明), Zhou Xin (周昕). Chin. Phys. B, 2015, 24(12): 120202.
[8]	Application of radial basis functions to evolution equations arising in image segmentation Li Shu-Ling (李淑玲), Li Xiao-Lin (李小林). Chin. Phys. B, 2014, 23(2): 028702.
[9]	Radiative decay from doubly to singly excited states of He via generalization of Laguerre-type orbitals: A non-orthogonal formalism Xiong Zhuang(熊庄) and Bacalis N C. Chin. Phys. B, 2007, 16(2): 374-381.
[10]	Group-theoretical method for physical property tensors of quasicrystals Gong Ping(龚平), Hu Cheng-Zheng(胡承正), Zhou Xiang(周详), Wang Ai-Jun(王爱军), and Miao Ling(缪灵). Chin. Phys. B, 2006, 15(9): 2065-2079.
[11]	Kondo effect for electron transport through an artificial quantum dot Sun Ke-Wei (孙科伟), Xiong Shi-Jie (熊诗杰). Chin. Phys. B, 2006, 15(4): 828-832.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Controllable precision of the projective truncation approximation for Green's functions

Cite this article:

Online attention