Mass-flow error in the numerical renormalization-group method and the critical behavior of the sub-Ohmic spin-boson model
Mass-flow error in the numerical renormalization-group method and the critical behavior of the sub-Ohmic spin-boson model
复制标题
DOI：
10.1103/physrevb.81.075122
复制
发表时间：
2009-11
影响因子：
3.7
通讯作者：
M. Vojta;R. Bulla;Fabian Guettge;F. Anders
中科院分区：
文献类型：
--
作者：
M. Vojta;R. Bulla;Fabian Guettge;F. Anders
我们讨论了量子杂质问题的数值重正化群 (NRG) 方法中的一个特定误差源，该误差与浴传播器引起的杂质参数的重正化有关。在 NRG 计算的任何步骤中，仅部分考虑这种重正化，导致杂质参数沿流动方向发生系统变化。在研究量子临界现象时，这种效应可能会导致定性上不正确的结果，因为它会导致相变控制参数作为温度函数的隐式变化，从而导致有序参数质量的非物理温度依赖性。我们用幂律浴谱证明了玻色子杂质模型的质量流效应，$J(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$，即耗散谐振子和自旋玻色子模型。我们提出了 NRG 的扩展来纠正质量流量误差。利用这一点，我们在 $sl1/2$ 的自旋玻色子模型中找到了高斯临界不动点的明确签名，与量子到经典映射所预期的平均场行为一致。
We discuss a particular source of error in the numerical renormalization group (NRG) method for quantum impurity problems, which is related to a renormalization of impurity parameters due to the bath propagator. At any step of the NRG calculation, this renormalization is only partially taken into account, leading to systematic variation in the impurity parameters along the flow. This effect can cause qualitatively incorrect results when studying quantum-critical phenomena, as it leads to an implicit variation in the phase transition's control parameter as function of the temperature and thus to an unphysical temperature dependence of the order-parameter mass. We demonstrate the mass-flow effect for bosonic impurity models with a power-law bath spectrum, $J(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$, namely, the dissipative harmonic oscillator and the spin-boson model. We propose an extension of the NRG to correct the mass-flow error. Using this, we find unambiguous signatures of a Gaussian critical fixed point in the spin-boson model for $sl1/2$, consistent with mean-field behavior as expected from quantum-to-classical mapping.