Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

doi:10.1088/1674-1056/26/6/060501

中国物理B ›› 2017, Vol. 26 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/26/6/060501

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华)

Department of Physics, Renmin University of China, Beijing 100872, China

收稿日期:2017-01-21 修回日期:2017-02-23 出版日期:2017-06-05 发布日期:2017-06-05
通讯作者: Ning-Hua Tong E-mail:nhtong@ruc.edu.cn
基金资助:
Project supported by the National 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).

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华)

Department of Physics, Renmin University of China, Beijing 100872, China

Received:2017-01-21 Revised:2017-02-23 Online:2017-06-05 Published:2017-06-05
Contact: Ning-Hua Tong E-mail:nhtong@ruc.edu.cn
Supported by:
Project supported by the National 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).

摘要/Abstract

摘要：

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω)∝ω^s is found to be universal and independent of the bias ε and the coupling strength α (except at the quantum critical point α=α_c and ε=0). Our NRG data also show C(ω)∝χ²ω^s for a wide range of parameters, including the biased strong coupling regime (ε≠0 and α > α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point α_c, the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω₀^* of the unbiased case. C(ω) is stable with respect to ε for ε≪ε^*. For ε≫ε^*, it is suppressed by ε in the low frequency regime. We establish that ε^*∝(ω₀^*)^1/θ holds for all sub-Ohmic regime 0≤s < 1, with θ=2/(3s) for 0 < s≤1/2 and θ=2/(1+s) for 1/2 < s < 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α-ε plane.

关键词: spin-boson model, numerical renormalization group, quantum phase transition, dynamical correlation function

Abstract:

Key words: spin-boson model, numerical renormalization group, quantum phase transition, dynamical correlation function

中图分类号: (Renormalization group methods)

05.10.Cc

05.30.Jp (Boson systems) 64.70.Tg (Quantum phase transitions) 75.20.Hr (Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions)

郑大川, 同宁华. Equilibrium dynamics of the sub-Ohmic spin-boson model under bias[J]. 中国物理B, 2017, 26(6): 60501-060501.

Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华). Equilibrium dynamics of the sub-Ohmic spin-boson model under bias[J]. Chin. Phys. B, 2017, 26(6): 60501-060501.

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Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

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