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arXiv:cond-mat/9507121 · Journal of the Physical Society of Japan

Exact Critical Exponents for Pseudo-Particles in the Kondo Problem

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

Published Dec 15, 1995• 10 citations
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Abstract

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.

DOI
10.1143/jpsj.64.4552

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Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU(NNN) Anderson model with U→∞U\rightarrow\inftyU→∞ 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.
We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.
Exact critical properties of the one-dimensional SU(N) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary conformal field theory. They are classified into two types, i.e., the exponents for the chiral SU(N) Tomonaga-Luttinger liquid and those related to the orthogonality catastrophe. We discuss a possible application of the results to the photoemission (absorption) in the edge state of the fractional quantum Hall effect. \textcopyright{} 1996 The American Physical Society.
We use the numerical renormalization group to calculate the auxiliary spectral functions of the $U=\ensuremath{\infty}$ Anderson impurity model. The slave-boson and pseudo-fermion spectral functions diverge at the threshold with exponents ${\ensuremath{\alpha}}_{b}$ and ${\ensuremath{\alpha}}_{f}$ given by the x-ray photoemission and the x-ray absorption exponents, respectively. In contrast to the noncrossing approximation, the exact exponents obtained here depend on the impurity occupation number. In general, vertex corrections in the convolution formulas for physical Green's functions are singular at the threshold and may not be neglected in the Fermi liquid regime.
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.
The finite-size spectrum in the Kondo problem is obtained from the Bethe-ansatz solution of the exactly solved models. We investigate the Anderson model, the highly correlated SU(\ensuremath{\nu}) Anderson model, and the s-d exchange model. For all these models we find that the spectra exhibit the properties characteristic of the Fermi-liquid fixed point, and hence our microscopic calculations are in accordance with the results obtained by boundary conformal field theory with current algebra symmetry.