论文标题
关于数值重归其化组的截断误差
On the Truncation Error of Numerical Renormalization Group
论文作者
论文摘要
使用最近开发的精确数值重归其化组（NRG）方法，我们分析了局部磁敏感性的NRG截断误差$Δχ$，以及Spin-Boson模型（SBM）的自由能的$ΔF$。我们发现，对于高于交叉温度$ t_ {cr} $的温度，随着保存状态的数量$ m $的增加，这两个错误都具有振荡，quasi osisi $ \ ln {m}/\ ln {n_b} $ and prespcemence and insevision andevelase andevelase hevelosees hisweasese an $ε_{tr} =λ^{ - \ ln {m}/\ ln {n_b}} $（$ n_b $是每个浴室使用的玻色子状态的数量）。对于$ t \ ll t_ {cr} $，它们降低的速度比电源定律慢。我们提取$ t_ {cr} = t^{\ ast}ε_{tr} $，其中$ t^{\ ast} $是SBM的解密和关键固定点之间的交叉能量尺度。同一规则适用于$Δχ$和$ΔF$从全密度矩阵NRG方法中计算出来的，预计将对一般杂质模型保存，从而可以准确地清除高温下静态数量的NRG截断误差。
Using the recently developed exact numerical renormalization group (NRG) method, we analyse the NRG truncation errors $δχ$ of the local magnetic susceptibility and $δF$ of the free energy for the spin-boson model (SBM). We find that for temperatures higher than a crossover temperature $T_{cr}$, as the number of kept states $M$ increases, both errors have oscillations with quasi period $\ln{M}/\ln{N_b}$ and the envelopes decrease as $ε_{tr}=Λ^{-\ln{M}/\ln{N_b}}$ ($N_b$ is the number of boson states used for each bath site). For $T \ll T_{cr}$, they decrease slower than the power law. We extract that $T_{cr} = T^{\ast} ε_{tr}$, with $T^{\ast}$ being the crossover energy scale between the declocalized and the critical fixed points of SBM. The same rule applies to $δχ$ and $δF$ calculated from the full density matrix NRG method and is expected to hold for general impurity models, allowing accurate removal of NRG truncation errors in static quantities at high temperatures.
