### 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 E. The crossover temperature TK=D(vxvz)12(vx4vz)14vz 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 vvy18. The crossover temperature can be found in the region of physical interest (TK>1 K) if the initial diagonal coupling vz>0.2. 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.

Original language | English |
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Pages (from-to) | 1582-1595 |

Number of pages | 14 |

Journal | Physical Review B |

Volume | 28 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

**Theory of the interaction between electrons and the two-level system in amorphous metals. II. Second-order scaling equations.** / Vladar, K.; Zawadowski, A.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 28, no. 3, pp. 1582-1595. https://doi.org/10.1103/PhysRevB.28.1582

}

TY - JOUR

T1 - Theory of the interaction between electrons and the two-level system in amorphous metals. II. Second-order scaling equations

AU - Vladar, K.

AU - Zawadowski, A.

PY - 1983

Y1 - 1983

N2 - 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 E. The crossover temperature TK=D(vxvz)12(vx4vz)14vz 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 vvy18. The crossover temperature can be found in the region of physical interest (TK>1 K) if the initial diagonal coupling vz>0.2. 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.

AB - 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 E. The crossover temperature TK=D(vxvz)12(vx4vz)14vz 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 vvy18. The crossover temperature can be found in the region of physical interest (TK>1 K) if the initial diagonal coupling vz>0.2. 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.

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U2 - 10.1103/PhysRevB.28.1582

DO - 10.1103/PhysRevB.28.1582

M3 - Article

VL - 28

SP - 1582

EP - 1595

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 3

ER -