Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

FIELD THEORY APPROACH TO CRITICAL QUANTUM IMPURITY PROBLEMS AND APPLICATIONS TO THE MULTI-CHANNEL KONDO EFFECT

Andreas W. W. Ludwig

Published Feb 14, 1994• 42 citations
Publisher

Abstract

A new, general approach to finding exact solutions of Quantum Impurity Problems is reviewed, in which a local quantum mechanical degree of freedom is coupled to an extended variable, having gapless excitations. The principle ideas, using Conformal Field Theory techniques, are demonstrated in the example of the Multi-Channel Kondo effect, which exhibits unusual non-Fermi-liquid behavior at low temperatures and which appears to be relevant for Heavy Fermion Materials. In particular, static and dynamic Green's functions as well as transport and pairing properties are calculated exactly at low temperatures. Quantum Impurity Problems provide realizations of non-trivial, fully interacting Conformal Field Theories.

DOI
10.1142/s0217979294000130

Related papers

Kondo Effect in a Luttinger Liquid: Exact Results from Conformal Field Theory

Per Fröjdh, Henrik Johannesson

We report on exact results for the low-temperature thermodynamics of a spin- $\frac{1}{2}$ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.

arXiv:cond-mat/9505100•Physical Review Letters•Jul 10, 1995•97 citations

Non-Fermi Liquid Behavior in Kondo Models

Ian K. Affleck

Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.

arXiv:cond-mat/0409173•Journal of the Physical Society of Japan•Jan 1, 2005•23 citations

Conformal Field Theory Approach to the Kondo Effect

Ian K. Affleck

Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem. In this review some earlier approaches to the Kondo problem are discussed, the needed material on boundary conformal field theory is developed and then this new method is applied to the multi-channel Kondo problem.

arXiv:cond-mat/9512099•Acta Physica Polonica B•Dec 12, 1995•124 citations

Quantum Impurity Problems in Condensed Matter Physics

Ian K. Affleck

Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.

arXiv:0809.3474•Sep 20, 2008•35 citations

Multichannel Kondo effect in an interacting electron system: Exact results for the low-temperature thermodynamics

Mats Granath, Henrik Johannesson

We study the low-temperature thermodynamics of a spin-$S$ magnetic impurity coupled to $m>~2$ 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 ${g}_{m}<~1$ is a generalized ($m$ 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 $(m=2S).$

arXiv:cond-mat/9710158•Physical review. B, Condensed matter•Jan 1, 1998•13 citations

Overscreened single-channel Kondo problem

Anirvan M. Sengupta, Yong Baek Kim

We consider the single-channel Kondo problem with the Kondo coupling between a spin $S$ impurity and conduction electrons with spin $j$. These problems arise as multicritical points in the parameter spaces of two-and higher-level tunneling systems and some impurity models of heavy fermion compounds. In contrast to the previous Bethe-ansatz conjectures, it turns out that the dynamics of the spin sector is the same as that of a spin-$S$ impurity coupled to $k(j)$ channels of spin-\textonehalf{} electrons with $k(j)=2\frac{j(j+1)(2j+1)}{3}$. As a result, for $2S<k(j)$, the system shows non-Fermi-liquid behavior with the same exponents for the thermodynamic quantities as those of the $k(j)$-channel Kondo problem. However, both the finite-size spectrum and the operator content are different due to the presence of the other sectors and can be obtained by conformal field theory techniques.

arXiv:cond-mat/9602100•Physical review. B, Condensed matter•Dec 1, 1996•19 citations
A new, general approach to finding exact solutions of Quantum Impurity Problems is reviewed, in which a local quantum mechanical degree of freedom is coupled to an extended variable, having gapless excitations. The principle ideas, using Conformal Field Theory techniques, are demonstrated in the example of the Multi-Channel Kondo effect, which exhibits unusual non-Fermi-liquid behavior at low temperatures and which appears to be relevant for Heavy Fermion Materials. In particular, static and dynamic Green's functions as well as transport and pairing properties are calculated exactly at low temperatures. Quantum Impurity Problems provide realizations of non-trivial, fully interacting Conformal Field Theories.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.
Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.
Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.
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).
We consider the single-channel Kondo problem with the Kondo coupling between a spin SSS impurity and conduction electrons with spin jjj. These problems arise as multicritical points in the parameter spaces of two-and higher-level tunneling systems and some impurity models of heavy fermion compounds. In contrast to the previous Bethe-ansatz conjectures, it turns out that the dynamics of the spin sector is the same as that of a spin-SSS impurity coupled to k(j)k(j)k(j) channels of spin-\textonehalf{} electrons with k(j)=2j(j+1)(2j+1)3k(j)=2\frac{j(j+1)(2j+1)}{3}k(j)=23j(j+1)(2j+1)​. As a result, for 2S<k(j)2S<k(j)2S<k(j), the system shows non-Fermi-liquid behavior with the same exponents for the thermodynamic quantities as those of the k(j)k(j)k(j)-channel Kondo problem. However, both the finite-size spectrum and the operator content are different due to the presence of the other sectors and can be obtained by conformal field theory techniques.