Instability of the marginal commutative model of tunneling centers interacting with metallic environment: Role of the electron-hole symmetry breaking

TL;DR

This paper investigates how electron-hole symmetry breaking affects the stability of the marginal commutative model of tunneling centers in metals, revealing that it can induce non-commutativity and assist tunneling but not enough to reach the two-channel Kondo fixed point.

Contribution

It provides a detailed analysis of symmetry breaking effects using multiplicative renormalization group and discusses differences with previous methods, highlighting implications for physical property calculations.

Findings

Electron-hole symmetry breaking induces non-commutativity.

Assisted tunneling is generated but insufficient for Kondo fixed point.

Differences in scaling equations impact physical quantity calculations.

Abstract

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), ibid 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.