arXiv:cond-mat/0411533 · Physical Review B

Two-channel Anderson impurity model: Single-electron Green’s function, self-energies, and resistivity

Henrik Johannesson, C. J. Bolech, Natan Andrei

Published May 18, 2005• 16 citations

Abstract

We compute exactly the low-energy single-electron Green's function, the impurity and electron self-energies, and the resistivity for the two-channel Anderson impurity model. These results are obtained by exploiting the boundary conformal field theory identified from the Bethe ansatz solution of the model. Using that solution we can make contact with the parameters of the original Hamiltonian and provide the detailed crossover between the two integer valence limits. Our results generalize those obtained previously in the context of the two-channel Kondo model.

DOI: 10.1103/physrevb.71.195107

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arXiv:cond-mat/0411533 · Physical Review B

Two-channel Anderson impurity model: Single-electron Green’s function, self-energies, and resistivity

Henrik Johannesson, C. J. Bolech, Natan Andrei

Published May 18, 2005• 16 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.71.195107

Related papers

Critical theory of the two-channel Anderson impurity model

Henrik Johannesson, Natan Andrei, C. J. Bolech

We construct the boundary conformal field theory that describes the low-temperature behavior of the two-channel Anderson impurity model. The presence of an exactly marginal operator is shown to generate a line of stable fixed points parametrized by the charge valence ${n}_{c}$ of the impurity. We calculate the exact zero-temperature entropy and impurity thermodynamics along the fixed line. We also derive the critical exponents of the characteristic Fermi edge singularities caused by time-dependent hybridization between conduction electrons and impurity. Our results suggest that in the mixed-valent regime ${(n}_{c}\ensuremath{\ne}0,1)$ the electrons participate in two competing processes, leading to frustrated screening of spin and channel degrees of freedom. By combining the boundary conformal field theory with the Bethe-Ansatz solution we obtain a complete description of the low-energy dynamics of the model.We construct the boundary conformal field theory that describes the low-temperature behavior of the two-channel Anderson impurity model. The presence of an exactly marginal operator is shown to generate a line of stable fixed points parametrized by the charge valence ${n}_{c}$ of the impurity. We calculate the exact zero-temperature entropy and impurity thermodynamics along the fixed line. We also derive the critical exponents of the characteristic Fermi edge singularities caused by time-dependent hybridization between conduction electrons and impurity. Our results suggest that in the mixed-valent regime ${(n}_{c}\ensuremath{\ne}0,1)$ the electrons participate in two competing processes, leading to frustrated screening of spin and channel degrees of freedom. By combining the boundary conformal field theory with the Bethe-Ansatz solution we obtain a complete description of the low-energy dynamics of the model.

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The impurity Green function and dynamical susceptibilities for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function as ratio of two correlation functions is given. The imaginary part of the self-energy scales as $\sqrt{\ensuremath{\mid}\ensuremath{\omega}∕{T}_{K}\ensuremath{\mid}}$ for $T\ensuremath{\rightarrow}0$, serving as a hallmark for non-Fermi behavior. The many-body resonance is pinned to a universal value of $1∕(2\ensuremath{\pi}\ensuremath{\Delta})$ at $\ensuremath{\omega}=0$ for arbitrary local occupation in contrary to the single-channel Anderson impurity model. Its shape becomes increasingly more symmetric for the Kondo regimes of the model. The dynamical spin and channel susceptibilities are governed by two energy scales ${T}_{K}$ and ${T}_{h}$ , and their ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ approach a constant value for $\ensuremath{\omega}\ensuremath{\rightarrow}0$.The impurity Green function and dynamical susceptibilities for the two-channel Anderson impurity model are calculated. An exact expression for the self-energy of the impurity Green function as ratio of two correlation functions is given. The imaginary part of the self-energy scales as $\sqrt{\ensuremath{\mid}\ensuremath{\omega}∕{T}_{K}\ensuremath{\mid}}$ for $T\ensuremath{\rightarrow}0$, serving as a hallmark for non-Fermi behavior. The many-body resonance is pinned to a universal value of $1∕(2\ensuremath{\pi}\ensuremath{\Delta})$ at $\ensuremath{\omega}=0$ for arbitrary local occupation in contrary to the single-channel Anderson impurity model. Its shape becomes increasingly more symmetric for the Kondo regimes of the model. The dynamical spin and channel susceptibilities are governed by two energy scales ${T}_{K}$ and ${T}_{h}$, and their ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ approach a constant value for $\ensuremath{\omega}\ensuremath{\rightarrow}0$.

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Satoshi Fujimoto, Norio Kawakami, S.-K. Yang

Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU( $N$ ) Anderson model with $U\rightarrow\infty$ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and Müller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU($N$) Anderson model with $U\rightarrow\infty$ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and Müller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.

arXiv:cond-mat/9507121Journal of the Physical Society of JapanDec 15, 199510 citations

{n}_{c}

of the impurity. We calculate the exact zero-temperature entropy and impurity thermodynamics along the fixed line. We also derive the critical exponents of the characteristic Fermi edge singularities caused by time-dependent hybridization between conduction electrons and impurity. Our results suggest that in the mixed-valent regime ${(n}_{c}\ensuremath{\ne}0,1)$ the electrons participate in two competing processes, leading to frustrated screening of spin and channel degrees of freedom. By combining the boundary conformal field theory with the Bethe-Ansatz solution we obtain a complete description of the low-energy dynamics of the model.

{T}^{2}, {V}^{2}

, and

{B}^{2}

are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

{T}_{K}

and

{T}_{h}

, and their ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ approach a constant value for $\ensuremath{\omega}\ensuremath{\rightarrow}0$.

Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU(

N

) Anderson model with

U\rightarrow\infty

are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and Müller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.