Following a recently proposed decomposition technique [C. R. Duan et al., Phys. Rev. B 95, 214308 (2017)], we inspect the zero-temperature spin-boson model for five different cutoff functions of the spectral density. With oscillatory and non-oscillatory exponentially decaying functions to decompose the bath correlation function, the hierarchy equation of motion is reliably extended to each spectral density under our investigation. The predicted spin dynamics is gradually converged with the increase of the hierarchic expansion order and the number of decomposing basis functions. Our systematic study of different cutoff functions expands previous results of the delocalized-localized phase transition with the exponential and sudden cutoffs in the spectral density.
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28 October 2017
Research Article|
October 27 2017
The study of an extended hierarchy equation of motion in the spin-boson model: The cutoff function of the sub-Ohmic spectral density
Chenru Duan
;
Chenru Duan
Physics Department, Zhejiang University
, Hangzhou, Zhejiang 310027, China
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Qianlong Wang;
Qianlong Wang
Physics Department, Zhejiang University
, Hangzhou, Zhejiang 310027, China
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Zhoufei Tang;
Zhoufei Tang
Physics Department, Zhejiang University
, Hangzhou, Zhejiang 310027, China
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Jianlan Wu
Jianlan Wu
a)
Physics Department, Zhejiang University
, Hangzhou, Zhejiang 310027, China
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a)
Electronic mail: jianlanwu@zju.edu.cn
J. Chem. Phys. 147, 164112 (2017)
Article history
Received:
July 26 2017
Accepted:
October 13 2017
Citation
Chenru Duan, Qianlong Wang, Zhoufei Tang, Jianlan Wu; The study of an extended hierarchy equation of motion in the spin-boson model: The cutoff function of the sub-Ohmic spectral density. J. Chem. Phys. 28 October 2017; 147 (16): 164112. https://doi.org/10.1063/1.4997669
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