Abstract
Effect of anharmonicity of a cage potential for a magnetic ion vibrating in a metal is investigated by the numerical renormalization group method. The cage potential is assumed to be one-dimensional and of the double-well type. In the absence of the Coulomb interaction, we find continuous crossover among the three limiting cases: Yu–Anderson-type Kondo regime, the double-well-type Kondo one, and the renormalized Fermi chain one. In the entire parameter space of the double-well potential, the ground state is described by a local Fermi liquid. In the Yu–Anderson-type Kondo regime, a quantum phase transition to the ground state with odd parity takes place passing through the two-channel Kondo fixed point when the Coulomb interaction increases. Therefore, the vibration of a magnetic ion in an oversized cage structure is a promising route to the two-channel Kondo effect.
Highlights
Many researchers in condensed matter physics have been interested in characteristic ionic structures, networks of cages filled or unfilled by guest ions
A very peculiar feature is observed in SmOs4Sb12.1–5) It is reported that a large specific heat coefficient γ is obtained, where the unusual phenomenon is its robustness against magnetic field.2) Some theoretical studies propose as a possible scenario that local vibrations of the guest ions lead to the nonmagnetic Kondo effect.6–8) In these theories, the authors consider the situation where the guest ion moves back and forth among several potential minima in the cage potential
We have studied the generalized Anderson model constructed for a magnetic ion vibrating in the double-well potential
Summary
Many researchers in condensed matter physics have been interested in characteristic ionic structures, networks of cages filled or unfilled by guest ions. The radius of filled ion is smaller than the size of cage In such a case, it is expected that they will show various unusual physical behaviors due to the vibrations of the guest ions in strongly anharmonic potential. We will study the effects of anharmonicity of a cage potential and discuss low-energy properties of a magnetic ion coupled with spinful conduction electrons. By applying numerical renormalization group method18, 19) to the present model, we find that in the noninteracting case, two types of nonmagnetic Kondo effect mentioned above are realized and the low-energy properties make continuous crossover between them when the shape of the cage potential is changed. We find that only in the typical YAK region, the 2-channel Kondo fixed point (2ch-K) appears with increasing U This behavior is similar to the harmonic potential case.
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