Department of Mathematics, Imperial College, London SW7 2AZ, UK.
J Phys Condens Matter. 2011 Feb 2;23(4):045601. doi: 10.1088/0953-8984/23/4/045601. Epub 2011 Jan 7.
The anomalous low energy behaviour observed in metals with strong electron correlation, such as in the heavy fermion materials, is believed to arise from the scattering of the itinerant electrons with low energy spin fluctuations. In systems with magnetic impurities this scattering leads to the Kondo effect and a low energy renormalized energy scale, the Kondo temperature T(K). It has been generally assumed that these low energy scales can only be accessed by a non-perturbative approach due to the strength of the local inter-electron interactions. Here we show that it is possible to circumvent this difficulty by first suppressing the spin fluctuations with a large magnetic field. As a first step field-dependent renormalized parameters are calculated using standard perturbation theory. A renormalized perturbation theory is then used to calculate the renormalized parameters for a reduced magnetic field strength. The process can be repeated and the flow of the renormalized parameters continued to zero magnetic field. We illustrate the viability of this approach for the single impurity Anderson model. The results for the renormalized parameters, which flow as a function of magnetic field, can be checked with those from numerical renormalization group and Bethe ansatz calculations.
在具有强电子关联的金属中观察到的异常低能行为，如重费米子材料中的行为，被认为是由巡游电子与低能自旋涨落的散射引起的。在具有磁性杂质的系统中，这种散射导致了近藤效应和低能重整化能标，即近藤温度 $T(K)$。由于局部电子相互作用的强度，通常假定这些低能标只能通过非微扰方法来获得。在这里，我们通过首先用大磁场抑制自旋涨落来绕过这个困难。作为第一步，使用标准微扰理论计算依赖于场的重整化参数。然后，使用重整化微扰理论来计算减小磁场强度的重整化参数。这个过程可以重复，并将重整化参数的流动延续到零磁场。我们用单杂质安德森模型来说明这种方法的可行性。作为磁场函数流动的重整化参数的结果，可以与数值重整化群和贝特假设计算的结果进行比较。
