Dynamical correlation functions of the quadratic coupling spin-Boson model  

作　　者：郑大川 同宁华 

机构地区：[1]Department of Physics, Renmin University of China, Beijing 100872, China

出　　处：《Chinese Physics B》2017年第6期81-86,共6页中国物理B（英文版）

基　　金：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;the Research Funds of Renmin University of China(Grant No.15XNLQ03)

摘　　要：The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, 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 = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-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 Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, 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 = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-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 Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

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

分 类 号：O413[理学—理论物理]