Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China.
J Chem Phys. 2019 Feb 28;150(8):084114. doi: 10.1063/1.5085871.
Through a decomposition of the bath correlation function, the hierarchical equations of motion are extended to the Ohmic spin-boson model at zero temperature. For two typical cutoff functions of the bath spectral density, the rate kernel of spin dynamics is numerically extracted by a time-convolution equation of the average magnetic moment. A characteristic time is defined accordingly as the inverse of the zeroth-order moment of the rate kernel. For a given Kondo parameter in the incoherent regime, the time evolution of average magnetic moments gradually collapses onto a master curve after rescaling the time variable with the characteristic time. The rescaled spin dynamics is nearly independent of the cutoff frequency and the form of cutoff functions. For a given cutoff frequency, the characteristic time with the change of the Kondo parameter is fitted excellently as a function of the renormalized tunneling amplitude. Despite a significant difference in definition, our result is in good agreement with the characteristic time of the noninteracting blip approximation.
通过对浴关联函数的分解，将层次运动方程扩展到零温度下的欧姆自旋-玻色子模型。对于浴谱密度的两个典型截止函数，通过平均磁矩的时间卷积方程数值提取自旋动力学的速率核。相应地定义了一个特征时间，作为速率核的零阶矩的倒数。在非相干区域中给定的近藤参数下，平均磁矩的时间演化在经过特征时间对时间变量进行缩放后逐渐收敛到主曲线。经过缩放的自旋动力学几乎与截止频率和截止函数的形式无关。对于给定的截止频率，随着近藤参数的变化，特征时间可以很好地拟合为重整化隧道振幅的函数。尽管定义上存在显著差异，但我们的结果与非相互作用的斑点近似的特征时间非常吻合。
