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Chin. Phys. B, 2008, Vol. 17(7): 2701-2706    DOI: 10.1088/1674-1056/17/7/057
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

A note on localized transition in the spin-boson model by variational calculation

Chen Zhi-De(陈芝得) and Hou Zhi-Lan(侯志兰)
Department of Physics, Jinan University, Guangzhou 510632, China
Abstract  We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as $J(\omega)=\pi\sum_k c_k^2=\dfrac{\pi}{2}\alpha \omega^{ s}\omega_{\rm c}^{ 1-s}$, there exists a universal $s_{\rm c}$ for both kinds of variational schemes, the localized transition happens only for $s\le s_{\rm c}$, moreover, the localized transition is discontinuous for $s<s_{\rm c}$ while a continuous transition always occurs when $s=s_{\rm c}$. At $T=0$, we have $s_{\rm c}=1$, while for $T\not=0$, $s_{\rm c}=2$ which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.
Keywords:  spin-boson model      localized transition      variational calculation  
Received:  14 January 2008      Revised:  27 February 2008      Accepted manuscript online: 
PACS:  05.30.Jp (Boson systems)  
  02.30.Xx (Calculus of variations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10575045).

Cite this article: 

Chen Zhi-De(陈芝得) and Hou Zhi-Lan(侯志兰) A note on localized transition in the spin-boson model by variational calculation 2008 Chin. Phys. B 17 2701

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