Low energy Fermi liquid approach for the Kondo problem

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.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.

arXiv:cond-mat/0409016Journal of the Physical Society of JapanJan 1, 200525 citations

TWO KONDO IMPURITY PROBLEM: RELEVANCE TO HEAVY FERMIONS

Barbara Jones, C. M. Varma

Elsevier eBooksJan 1, 19871 citation

Instability of the Fermi-Liquid Fixed Point in an Extended Kondo Model

M. Lavagna, Andrés Jerez, Damien Bensimon

arXiv:cond-mat/0302192Springer eBooksJan 1, 20031 citation

Non-Fermi liquid, unscreened scalar chirality, and parafermions in a frustrated tetrahedron Anderson model

Kazumasa Hattori, Hirokazu Tsunetsugu

We investigate a four-impurity Anderson model where localized orbitals are located at vertices of a regular tetrahedron and find a novel fixed point in addition to the ordinary Fermi liquid phase. That is characterized by unscreened scalar chirality of a tetrahedron. In this phase, parafermions emerge in the excitation spectrum and quasiparticle mass diverges as $1/|T{\mathrm{ln}}^{3}T|$ at low temperatures ( $T$ ). The diverging effective mass is a manifestation of singular Fermi liquid states as in the underscreened Kondo problem. Between the two phases, our Monte Carlo results show the existence of a non-Fermi liquid critical point where the Kondo effects and the intersite antiferromagnetic interactions are valanced. Singular behaviors are prominent in the dynamics and we find that the frequency dependence of the self-energy is the marginal Fermi liquid like $\ensuremath{-}\mathrm{Im}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Sigma}\ensuremath{\sim}|\ensuremath{\omega}|$.We investigate a four-impurity Anderson model where localized orbitals are located at vertices of a regular tetrahedron and find a novel fixed point in addition to the ordinary Fermi liquid phase. That is characterized by unscreened scalar chirality of a tetrahedron. In this phase, parafermions emerge in the excitation spectrum and quasiparticle mass diverges as $1/|T{\mathrm{ln}}^{3}T|$ at low temperatures ($T$). The diverging effective mass is a manifestation of singular Fermi liquid states as in the underscreened Kondo problem. Between the two phases, our Monte Carlo results show the existence of a non-Fermi liquid critical point where the Kondo effects and the intersite antiferromagnetic interactions are valanced. Singular behaviors are prominent in the dynamics and we find that the frequency dependence of the self-energy is the marginal Fermi liquid like $\ensuremath{-}\mathrm{Im}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Sigma}\ensuremath{\sim}|\ensuremath{\omega}|$.

arXiv:1207.6262Physical Review BAug 15, 20123 citations

Non-Fermi-liquid quantum impurity physics from non-Abelian quantum Hall states

Stuart A. Sevier, Gregory A. Fiete

We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [Fiete, Bishara, and Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multichannel Kondo fixed point at low energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi-liquid properties. Previously unidentified fixed points may also be among the possibilities. We examine both the situation where the dots are spatially separated and where they are in close proximity. We discuss the relation to previous work on two-impurity Kondo models in Fermi liquids and highlight new research directions in multiple quantum impurity problems.We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [Fiete, Bishara, and Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multichannel Kondo fixed point at low energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi-liquid properties. Previously unidentified fixed points may also be among the possibilities. We examine both the situation where the dots are spatially separated and where they are in close proximity. We discuss the relation to previous work on two-impurity Kondo models in Fermi liquids and highlight new research directions in multiple quantum impurity problems.

arXiv:1101.1326Physical Review BJul 11, 20112 citations

1/|T{\mathrm{ln}}^{3}T|

at low temperatures (

T

). The diverging effective mass is a manifestation of singular Fermi liquid states as in the underscreened Kondo problem. Between the two phases, our Monte Carlo results show the existence of a non-Fermi liquid critical point where the Kondo effects and the intersite antiferromagnetic interactions are valanced. Singular behaviors are prominent in the dynamics and we find that the frequency dependence of the self-energy is the marginal Fermi liquid like $\ensuremath{-}\mathrm{Im}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Sigma}\ensuremath{\sim}|\ensuremath{\omega}|$.