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arXiv:cond-mat/9710262

Low Temperature Behavior of the Kondo Effect in Tomonaga-Luttinger Liquid

Yu-Liang Liu

Published Oct 24, 1997• 0 citations
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Abstract

Using the bosonization method, we study the low temperature behavior of the Kondo effect in the Tomonaga-Luttinger liquid and clearly show that the power law temperature dependence of the impurity susceptibility is completely determined by the repulsive electron-electron interaction existing in the total spin channel and is independent of the electron-electron interaction existing in the charge channels.

DOI
10.48550/arxiv.cond-mat/9710262

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Using the bosonization method, we study the low temperature behavior of the Kondo effect in the Tomonaga-Luttinger liquid and clearly show that the power law temperature dependence of the impurity susceptibility is completely determined by the repulsive electron-electron interaction existing in the total spin channel and is independent of the electron-electron interaction existing in the charge channels.
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A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, gc<12{g}_{c}<\frac{1}{2}gc​<21​, and anomalous power laws for 12<gc<1\frac{1}{2}<{g}_{c}<121​<gc​<1, where gc{g}_{c}gc​ is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at gc<12{g}_{c}<\frac{1}{2}gc​<21​ that can be rationalized in terms of the two-channel Kondo model.
Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed with emphasis on their analogy to the Kondo problem in Fermi liquids. First, the problem of a static impurity in a spinless TLL is considered, which is related to the model studied in the context of the macroscopic quantum coherence. In the low-energy limit the TLL is essentially cut into two pieces when interaction is repulsive. The orthogonality catastrophe in a TLL is then discussed. Finally, the Kondo effect of a spin-1/2 impurity in a one-dimensional repulsively interacting electron liquids (a spinful TLL) is reviewed. Regardless of the sign of the exchange coupling, the impury spin is completely screened in the ground state. The leading low-temperature contributions to thermodynamic quantities come from boundary contributions of a bulk leading irrelevant operator.
We study the low-temperature thermodynamics of a spin-SSS magnetic impurity coupled to m> 2m>~2m> 2 degenerate bands of interacting electrons in one dimension. By exploiting boundary-conformal-field-theory techniques, we derive exact results for the possible impurity thermal and magnetic response. The leading behavior of the impurity magnetic susceptibility is shown to be insensitive to the electron-electron interaction. In contrast, there are two types of scaling behavior of the impurity specific heat consistent with the symmetries of the problem: Either it remains the same as for the ordinary multichannel Kondo problem for noninteracting electrons or it acquires a new leading term governed by a critical exponent ${\ensuremath{\alpha}}_{m}{=(g}_{m}^{\ensuremath{-}1}\ensuremath{-}1)/m,$ where gm< 1{g}_{m}<~1gm​< 1 is a generalized (mmm channel) Luttinger-liquid charge parameter measuring the strength of the repulsive electron-electron interaction. We conjecture that the latter behavior is indeed realized when the impurity is exactly screened (m=2S).(m=2S).(m=2S).
The Kondo effect in a Luttinger liquid composed of right-moving, spin-up electrons and left-moving, spin-down electrons is mapped exactly onto the Kondo effect in a Fermi liquid. The transformation generates anisotropy in the exchange coupling, which explains the two most notable features of the Kondo effect in a full Luttinger liquid: the quenching of the impurity moment for ferromagnetic, as well as antiferromagnetic, exchange and a power-law dependence of the Kondo temperature on the exchange coupling. Impurity contributions to the low-energy thermodynamics have the same temperature dependence as in a Fermi liquid.