Abstract
A general Hamiltonian for the interaction between conduction electrons and the two-level system is considered. Renormalization-group equations of second order are constructed with the use of the multiplicative renormalization-group technique. The mass renormalization is treated in detail to determine the effect of screening by conduction electrons on the energy splitting . The crossover temperature between the weak and strong coupling regions is determined, and it is reduced by 2 orders of magnitude compared to the expression obtained in first-order scaling. The scaled values of the couplings are calculated analytically. In the crossover region the off-diagonal couplings are . The crossover temperature can be found in the region of physical interest ( K) if the initial diagonal coupling . In this case, the energy splitting calculated is reduced by more than 2 orders of magnitude. That reduction results in a large enhancement in the distribution of the energy splitting at the low-energy side. The position of the lower end of the scaling region is discussed where scaling in terms of temperature is hindered by the energy splitting.
- Received 10 June 1982
DOI:https://doi.org/10.1103/PhysRevB.28.1582
©1983 American Physical Society