Numerical Calculation of the Fidelity for the Kondo and the Friedel-Anderson Impurities
arXiv:1109.2670 · doi:10.1140/epjb/e2011-20727-3
Abstract
The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N_{eff} when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a, 05.30.-d
References in corpus (8)
- The numerical renormalization group method for quantum impurity systems
- Quantum critical scaling of the geometric tensors
- Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
- Quantum phase transitions and quantum fidelity in free fermion graphs
- Finite temperature fidelity susceptibility for one-dimensional quantum systems
- Quantitative Calculation of the Spatial Extension of the Kondo Cloud
- A Compact Approximate Solution to the Kondo Problem
- A Compact Approximate Solution to the Friedel-Anderson Impuriy Problem