We present results for the Kondo effect in two crossed Luttinger liquids by using boundary conformal field theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio or a theory with an anomalous reponse that is identical to that found by Furusaki and Nagaosa for the Kondo effect in a single Luttinger liquid. Moreover, we discuss the relevance of perturbations like channel anisotropy in restoring a Fermi-liquid-like Kondo fixed point, and compare our results with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory. Consequences are discussed.We present results for the Kondo effect in two crossed Luttinger liquids by using boundary conformal field theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio or a theory with an anomalous reponse that is identical to that found by Furusaki and Nagaosa for the Kondo effect in a single Luttinger liquid. Moreover, we discuss the relevance of perturbations like channel anisotropy in restoring a Fermi-liquid-like Kondo fixed point, and compare our results with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory. Consequences are discussed.

arXiv:cond-mat/9910372Physical review. B, Condensed matterJan 15, 20007 citations

Influence of the Kondo effect in a non-Fermi liquid system

Karyn Le Hur

The Kondo effect in a Tomonaga-Luttinger liquid ($U<

arXiv:cond-mat/9802298Feb 27, 19980 citations

Quantum dot in a two-dimensional topological insulator: The two-channel Kondo fixed point

K. T. Law, Chien-Yeah Seng, Patrick A. Lee +1 more

A quantum dot coupled to two helical edge states of a two-dimensional topological insulator through electron tunnelings is studied. We show that if the electron interactions on the edge states are repulsive, with Luttinger liquid parameter $K<1$ , the system reaches a stable two-channel Kondo fixed point at low temperatures. This is in contrast to the Luttinger liquid leads case in which $K<1/2$ is needed. This two-channel fixed point is described by a boundary sine-Gordon Hamiltonian with a $K$ dependent boundary term. The impurity entropy, the impurity specific heat and the conductance are calculated.A quantum dot coupled to two helical edge states of a two-dimensional topological insulator through electron tunnelings is studied. We show that if the electron interactions on the edge states are repulsive, with Luttinger liquid parameter $K<1$, the system reaches a stable two-channel Kondo fixed point at low temperatures. This is in contrast to the Luttinger liquid leads case in which $K<1/2$ is needed. This two-channel fixed point is described by a boundary sine-Gordon Hamiltonian with a $K$ dependent boundary term. The impurity entropy, the impurity specific heat and the conductance are calculated.

arXiv:0904.2262Physical Review BJan 14, 201041 citations

Luttinger sum rules in the 2-channel spin 1 Kondo chain

Ian P. McCulloch

Bulletin of the American Physical SocietyMar 15, 20060 citations

Charge Kondo circuit as a detector for electron-electron interactions in a Luttinger liquid

T. K. T. Nguyen, Anton V. Parafilo, H. Q. Nguyen +1 more

We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area $L$ in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot $a$ . We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area $L$ in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot $a$. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.

arXiv:2212.10383Physical review. B./Physical review. BMay 9, 20237 citations

K<1

, the system reaches a stable two-channel Kondo fixed point at low temperatures. This is in contrast to the Luttinger liquid leads case in which

K<1/2

is needed. This two-channel fixed point is described by a boundary sine-Gordon Hamiltonian with a

K

dependent boundary term. The impurity entropy, the impurity specific heat and the conductance are calculated.

L

in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot

a

. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.