The role of the electron-hole symmetry breaking is investigated for a symmetrical commutative two-level system in a metal using the multiplicative renormalization group in a straightforward way. The role of the symmetries of the model and the path-integral technique are also discussed in detail. It is shown that the electron-hole symmetry breaking may make the model non-commutative and generate the assisted tunneling process which is, however, too small itself to drive the system into the vicinity of the two-channel Kondo fixed point. While these results are in qualitative agreement with those of Moustakas and Fisher [Phys. Rev. B 51, 6908 (1995); 53, 4300 (1996)], the scaling equations turn out to be essentially different. We show that the main reason for this difference is that the procedure for the elimination of the high-energy degrees of freedom used by Moustakas and Fisher leaves only the free-energy invariant, however, the couplings generated are not connected to the dynamical properties in a straightforward way and should be interpreted with care. These latter results might have important consequences in other cases where the path-integral technique is used to produce the scaling equations and calculate physical quantities.
|Number of pages||14|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - jan. 1 1997|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics