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

arXiv:1212.5179 · Physical Review B

Overscreened Kondo fixed point in S=1 spin liquid

Maksym Serbyn, T. Senthil, Patrick A. Lee

Published Jul 19, 2013• 4 citations
arXivHTMLPDF

Abstract

We propose a possible realization of the overscreened Kondo impurity problem by a magnetic $s=1/2$ impurity embedded in a two-dimensional $S=1$ $U(1)$ spin liquid with a Fermi surface. This problem contains an interesting interplay between non-Fermi-liquid behavior induced by a $U(1)$ gauge field coupled to fermions and a non-Fermi-liquid fixed point in the overscreened Kondo problem. Using a large-$N$ expansion together with an expansion in the dynamical exponent of the gauge field, we find that the coupling to the gauge field leads to weak but observable changes in the physical properties of the system at the overscreened Kondo fixed point. We discuss the extrapolation of this result to a physical case and argue that the realization of overscreened Kondo physics could lead to observations of effects due to gauge fields.

DOI
10.1103/physrevb.88.024419

Related papers

The Kondo impurity in the large spin limit

Abijith Krishnan, Max A. Metlitski

The Kondo problem, which describes the interaction of a spin $s$ magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in $1/s$ with the renormalization group. We study both the case of an impurity interacting with a single channel $K=1$ of fermions in the $s \rightarrow \infty$ limit and the case with $K$ channels in the double-scaling limit $K \rightarrow \infty$, $s \to \infty$, $K/s$ fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large $s$ and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime $K > 2s$ we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.

arXiv:2408.12650•Aug 22, 2024•0 citations

Magnetic impurity in a U ( 1 ) spin liquid with a spinon Fermi surface

Pedro Ribeiro, Patrick A. Lee

We address the problem of a magnetic impurity in a two-dimensional $U(1)$ spin liquid where the spinons have gapless excitations near the Fermi surface and are coupled to an emergent gapless gauge field. Using a large N expansion, we analyze the strong coupling behavior and obtain the Kondo temperature which was found to be the same as for a Fermi liquid. In this approximation, we also study the specific heat and the magnetic susceptibility of the impurity. These quantities present no deviations from the Fermi liquid ones, consistent with the notion that the magnetic impurity is only sensitive to the local density of fermionic states.

arXiv:1012.2988•Physical Review B•Jun 10, 2011•29 citations

Model for overscreened Kondo effect in ultracold Fermi gas

Igor Kuzmenko, Tetyana Kuzmenko, Y. Avishai +1 more

The feasibility of realizing the overscreened Kondo effect in ultracold Fermi gas of atoms with spin $s\ensuremath{\ge}\frac{3}{2}$ in the presence of a localized magnetic impurity atom is proved realistic. Specifying (as a mere example) a system of ultracold $^{22}\mathrm{Na}$ Fermi gas and a trapped $^{6}\mathrm{Li}$ impurity, the mechanism of exchange interaction between the Na and Li atoms is elucidated and the exchange constant is found to be positive (antiferromagnetic). The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of 500 nK. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi-liquid fixed point. An observable displaying multichannel features even in the weak-coupling regime is the impurity magnetization that is negative for $T\ensuremath{\gg}{T}_{K}$ and becomes positive with decreasing temperature.

arXiv:1402.0187•Physical Review B•Apr 27, 2015•15 citations

Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models

Damien Bensimon, Andrés Jerez, M. Lavagna

We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the $\mathrm{SU}(N)$ group that combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov that allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\ensuremath{\beta}$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozi\`eres-Blandin) regime, for an arbitrary $\mathrm{SU}(N)$ group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low $T$, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric, and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of $\mathrm{SU}(N)$ are also discussed.

arXiv:cond-mat/0601144•Physical Review B•Jun 30, 2006•15 citations

Non-Fermi-liquid behavior in quantum impurity models with superconducting channels

Rok Žitko, Michele Fabrizio

We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap $\mathrm{\ensuremath{\Delta}}$. We find that the low-energy spectrum in the limit $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ actually does not correspond to the spectrum strictly at $\mathrm{\ensuremath{\Delta}}=0$. In particular, in the two-channel Kondo model, the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at $\mathrm{\ensuremath{\Delta}}=0$. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of $\mathrm{\ensuremath{\Delta}}$ tends toward a finite and universal value when $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by $\mathrm{\ensuremath{\Delta}}\ensuremath{\ne}0$. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite $\mathrm{\ensuremath{\Delta}}$: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.

arXiv:1606.07697•Physical review. B./Physical review. B•Feb 16, 2017•13 citations

Overscreened Kondo problem with large spin and large number of orbital channels: Two distinct semiclassical limits in quantum transport observables

D. B. Karki, Mikhail N. Kiselev

We investigate quantum transport through the Kondo impurity assuming both a large number of orbital channels $\mathcal{K}\ensuremath{\gg}1$ for the itinerant electrons and a semiclassical spin $\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$ for the impurity. The non-Fermi-liquid regime of the Kondo problem is achieved in the overscreened sector $\mathcal{K}>2\mathcal{S}$. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: (i) $\mathcal{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$, differential conductance vanishes, and (ii) $\mathcal{S}/\mathcal{K}=\mathcal{C}$ with $0<\mathcal{C}<1/2$, differential conductance reaches some nonvanishing fraction of its unitary value. Using the conformal field theory approach we analyze the behavior of the quantum transport observables and residual entropy in both semiclassical regimes. We show that the semiclassical limit (ii) preserves the key features of resonance scattering and the most essential fingerprints of the non-Fermi-liquid behavior. We discuss possible realization of two semiclassical regimes in semiconductor quantum transport experiments.

arXiv:2103.12500•Physical review. B./Physical review. B•May 14, 2021•1 citation
We propose a possible realization of the overscreened Kondo impurity problem by a magnetic s=1/2s=1/2s=1/2 impurity embedded in a two-dimensional S=1S=1S=1 U(1)U(1)U(1) spin liquid with a Fermi surface. This problem contains an interesting interplay between non-Fermi-liquid behavior induced by a U(1)U(1)U(1) gauge field coupled to fermions and a non-Fermi-liquid fixed point in the overscreened Kondo problem. Using a large-NNN expansion together with an expansion in the dynamical exponent of the gauge field, we find that the coupling to the gauge field leads to weak but observable changes in the physical properties of the system at the overscreened Kondo fixed point. We discuss the extrapolation of this result to a physical case and argue that the realization of overscreened Kondo physics could lead to observations of effects due to gauge fields.
The Kondo problem, which describes the interaction of a spin sss magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in 1/s1/s1/s with the renormalization group. We study both the case of an impurity interacting with a single channel K=1K=1K=1 of fermions in the s→∞s \rightarrow \inftys→∞ limit and the case with KKK channels in the double-scaling limit K→∞K \rightarrow \inftyK→∞, s→∞s \to \inftys→∞, K/sK/sK/s fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large sss and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime K>2sK > 2sK>2s we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.
We address the problem of a magnetic impurity in a two-dimensional U(1)U(1)U(1) spin liquid where the spinons have gapless excitations near the Fermi surface and are coupled to an emergent gapless gauge field. Using a large N expansion, we analyze the strong coupling behavior and obtain the Kondo temperature which was found to be the same as for a Fermi liquid. In this approximation, we also study the specific heat and the magnetic susceptibility of the impurity. These quantities present no deviations from the Fermi liquid ones, consistent with the notion that the magnetic impurity is only sensitive to the local density of fermionic states.
The feasibility of realizing the overscreened Kondo effect in ultracold Fermi gas of atoms with spin $s\ensuremath{\ge}\frac{3}{2}$ in the presence of a localized magnetic impurity atom is proved realistic. Specifying (as a mere example) a system of ultracold 22Na^{22}\mathrm{Na}22Na Fermi gas and a trapped 6Li^{6}\mathrm{Li}6Li impurity, the mechanism of exchange interaction between the Na and Li atoms is elucidated and the exchange constant is found to be positive (antiferromagnetic). The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of 500 nK. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi-liquid fixed point. An observable displaying multichannel features even in the weak-coupling regime is the impurity magnetization that is negative for $T\ensuremath{\gg}{T}_{K}$ and becomes positive with decreasing temperature.
We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the SU(N)\mathrm{SU}(N)SU(N) group that combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov that allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\ensuremath{\beta}$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozi\`eres-Blandin) regime, for an arbitrary SU(N)\mathrm{SU}(N)SU(N) group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low TTT, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric, and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of SU(N)\mathrm{SU}(N)SU(N) are also discussed.
We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap $\mathrm{\ensuremath{\Delta}}$. We find that the low-energy spectrum in the limit $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ actually does not correspond to the spectrum strictly at $\mathrm{\ensuremath{\Delta}}=0$. In particular, in the two-channel Kondo model, the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at $\mathrm{\ensuremath{\Delta}}=0$. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of $\mathrm{\ensuremath{\Delta}}$ tends toward a finite and universal value when $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by $\mathrm{\ensuremath{\Delta}}\ensuremath{\ne}0$. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite $\mathrm{\ensuremath{\Delta}}$: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.
We investigate quantum transport through the Kondo impurity assuming both a large number of orbital channels $\mathcal{K}\ensuremath{\gg}1$ for the itinerant electrons and a semiclassical spin $\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$ for the impurity. The non-Fermi-liquid regime of the Kondo problem is achieved in the overscreened sector K>2S\mathcal{K}>2\mathcal{S}K>2S. We show that there exist two distinct semiclassical regimes for the quantum transport through impurity: (i) $\mathcal{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}\mathcal{S}\phantom{\rule{4pt}{0ex}}\ensuremath{\gg}\phantom{\rule{4pt}{0ex}}1$, differential conductance vanishes, and (ii) S/K=C\mathcal{S}/\mathcal{K}=\mathcal{C}S/K=C with 0<C<1/20<\mathcal{C}<1/20<C<1/2, differential conductance reaches some nonvanishing fraction of its unitary value. Using the conformal field theory approach we analyze the behavior of the quantum transport observables and residual entropy in both semiclassical regimes. We show that the semiclassical limit (ii) preserves the key features of resonance scattering and the most essential fingerprints of the non-Fermi-liquid behavior. We discuss possible realization of two semiclassical regimes in semiconductor quantum transport experiments.