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arXiv:cond-mat/9401059 · Physical review. B, Condensed matter

Asymptotically exact solution of the multichannel resonant-level model

Guang-Ming Zhang, Zhao-Bin Su, Lu Yu

Published Mar 15, 1994• 9 citations
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Abstract

An asymptotically exact partition function of the multichannel resonant-level model is obtained through Tomonaga-Luttinger bosonization. A Fermi-liquid vs non-Fermi-liquid transition, resulting from a competition between the Kondo resonance and the x-ray edge singularity, is elucidated explicitly via renormalization-group theory. In the strong-coupling limit, the model is renormalized to the Toulouse limit.

DOI
10.1103/physrevb.49.7759

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An asymptotically exact partition function of the multichannel resonant-level model is obtained through Tomonaga-Luttinger bosonization. A Fermi-liquid vs non-Fermi-liquid transition, resulting from a competition between the Kondo resonance and the x-ray edge singularity, is elucidated explicitly via renormalization-group theory. In the strong-coupling limit, the model is renormalized to the Toulouse limit.
We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength UT{\mathit{U}}_{\mathit{T}}UT​ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.
We present an asymptotically exact solution of a local copper-oxide model abstracted from the multiband models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities.
The $\ensuremath{\beta}$ function of the multichannel Kondo model is calculated exactly in the limit of large spin N and channel number $M=\ensuremath{\gamma}N$, with constant $\ensuremath{\gamma}$. There are no corrections in any finite order of 1/N1/N1/N. One zero is found at a finite coupling strength, showing directly the non-Fermi-liquid behavior of the model. This renormalization group flow allows introduction of a variational principle for the entropy, to obtain the low-temperature thermodynamics. Thus, in particular, the low-temperature thermodynamics of the noncrossing approximation to the Kondo model becomes accessible.
Exact 3D space- and time-dependent Green's functions are computed for the multichannel Kondo effect in the universal large-distance, long-time regime, using conformal field theory. They exhibit crossover from Fermi-liquid form far away, to singular non-Fermi-liquid behavior, near the impurity, where charge, spin, and ``flavor'' degrees of freedom become ``deconfined.'' Explicit expressions are given for the resistivity, \ensuremath{\rho}, for all k and for the spin-density and pair-density Green's functions, for k=2. For k=2, \ensuremath{\rho}(T)-\ensuremath{\rho}(0)\ensuremath{\propto}T1/2{\mathit{T}}^{1/2}T1/2 and the pair susceptibility \ensuremath{\propto}lnT.
We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant-level model. Limiting cases in which the equivalent resonant-level model is solvable are identified. The solution correctly captures the properties of the two-channel Kondo model, and also allows an analytic description of the crossover from the non-Fermi-liquid to the Fermi-liquid behavior caused by the channel anisotropy.
We report the exact calculation of the Fermi-edge singularity exponent for correlated electrons in one dimension (Luttinger liquid). Focusing on the special interaction parameter g=1/2g=1/2g=1/2, the asymptotic long-time behavior can be obtained using the Wiener-Hopf method. The result confirms the previous assumption of an open boundary fixed point. In addition, a dynamic kkk-channel Kondo impurity is studied via Abelian bosonization for k=2k=2k=2 and k=4k=4k=4. It is shown that the corresponding orthogonality exponents are related to the orthogonality exponent in a Luttinger liquid.