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

  title={Instability of the marginal commutative model of tunneling centers interacting with a metallic environment: Role of the electron-hole symmetry breaking},
  author={Alfred Zawadowski and Gergely Zar{\'a}nd and Philippe Nozi{\`e}res and K. Vlad{\'a}r and Gergely T. Zim{\'a}nyi},
  journal={Physical Review B},
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… 
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