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:cond-mat/9907166 · Journal of the Physical Society of Japan

Crossover between Fermi Liquid and Non-Fermi Liquid in Orbitally Degenerate Kondo Systems

Hiroaki Kusunose, Yoshio Kuramoto

Published Dec 15, 1999• 3 citations
arXivHTMLPDF

Abstract

Entanglement of spin and orbital Kondo effect is investigated on the basis of a Kondo-type exchange model with twofold orbital degeneracy. By using Wilson's numerical renormalization-group method, we examine dynamical and thermal properties respecting the difference in time-reversal property of multipole operators. In the presence of particle-hole symmetry, the model has a new non-Fermi-liquid fixed point with a fractional entropy. The spectral intensity of the quadrupole susceptibility diverges in the zero-frequency limit, while the dipole susceptibility shows a Fermi-liquid-like behavior. This is understood by mapping to the two-channel Kondo model, in which the dipole moment is mapped onto the operators with the scaling dimension $Δ_m=1$, while the quadrupole moment onto the operators with another scaling dimension $Δ_e=1/2$. Even for a fairly particle-hole asymmetric case with the Fermi-liquid ground state, the non-Fermi-liquid behavior has significant influences in electric and thermal properties.

DOI
10.1143/jpsj.68.3960

Related papers

Crossover Temperature from Non-Fermi Liquid to Fermi Liquid Behavior in Two Types of Impurity Kondo Model

Satoshi Yotsuhashi, Hideaki Maebashi

Numerical renormalization-group results on entropy of the anisotropic two-channel Kondo model with the band-width cutoff ($D$) in the presence of a magnetic field ($h$) are obtained to determine crossover temperature from the non-Fermi liquid to Fermi liquid fixed point. It is found that the crossover temperature ($T_{\rm x}$) is given by $T_{\rm x} \equiv {r} T_{\rm K} \sim D(ΔJ/J_{\rm av})^2 e^{-1/J_{\rm av}}$ when $(h /T_{\rm K})^2 \ll r \ll 1 $, where $T_{\rm K}$, $J_{\rm av}$ and $ΔJ$ are the Kondo temperature, the average and difference of the exchange coupling constants, respectively. This result indicates that non-Fermi liquid behavior can be seen even if $ΔJ > T_{\rm K}$. Robust similarities of the crossover behavior in the region around the non-Fermi liquid critical point to that of the two-impurity Kondo model are also discussed.

arXiv:cond-mat/0203506•Journal of the Physical Society of Japan•Jul 15, 2002•12 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

Non-Fermi-Liquid States in a Generalized Two-Channel Kondo Model

Hanbin Pang

Using the numerical renormalization group method, we study a generalized two-channel Kondo model where the impurity has a quadrupole moment (pseudospin) and a magnetic moment (flavor). This model may be of relevance to the Ce ions in ${\mathrm{CeB}}_{6}$ and the Cu ions in cuprate superconductors. We find that the nontrivial fixed point of the two-channel Kondo model is unstable against flavor exchange coupling. The system flows to a non-Fermi-liquid fixed line. In the presence of a double tensor interaction, which breaks particle-hole symmetry, the system flows to a Fermi-liquid fixed line.

Physical Review Letters•Nov 14, 1994•14 citations

Spectral properties of a two-orbital Anderson impurity model across a non-Fermi-liquid fixed point

Lorenzo De Leo, Michele Fabrizio

We study by Wilson numerical renormalization group the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting that follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi-liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudogap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also consider the effect of several particle-hole symmetry-breaking terms. We show that particle-hole perturbations that simply shift the orbital energies do not wash out the fixed point, unlike those perturbations that hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry. In other words, the pseudogap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models that map onto this Anderson impurity model in the limit of large lattice coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality that reflects the impurity non-Fermi-liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk coherent symmetry-broken phases, which we identify for different lattice models.

arXiv:cond-mat/0402121•Physical Review B•Jun 25, 2004•50 citations

Two-channel pseudogap Kondo and Anderson models: Quantum phase transitions and non-Fermi liquids

Imke Schneider, Lars Fritz, Frithjof B. Anders +2 more

We discuss the two-channel Kondo problem with a pseudogap density of states $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{|\ensuremath{\omega}|}^{r}$ of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi-liquid behavior of the metallic $r=0$ case, is replaced by a stable particle-hole-symmetric intermediate-coupling fixed point for $0<r<{r}_{\mathrm{max}}\ensuremath{\approx}0.23$. For $r>{r}_{\mathrm{max}}$, this non-Fermi-liquid phase disappears, and instead a critical fixed point with an emergent spin-channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose low-energy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ $\ensuremath{\epsilon}$ expansion techniques to calculate critical properties near the critical dimensions $r=0$ and 1, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.

arXiv:1108.2213•Physical Review B•Sep 29, 2011•18 citations

Topological ground state degeneracy of the two-channel Kondo lattice

Aleksandar Ljepoja, Yashar Komijani

There has been significant recent interest in the potential exotic properties of multichannel Kondo lattices and their connection to quantum materials, but the strongly coupled nature of these models has posed challenges to theoretical investigations. We study the emergence of topological order in a two-dimensional two-channel Kondo lattice (2CKL) in a time-reversal symmetry-broken channel symmetric phase using a coupled-wire construction from one-dimensional (1D) 2CKLs. Through bosonization and symmetry analysis, we show that away from particle-hole symmetry, the 1D 2CKL model flows to an infrared fixed point with an emergent $\mathrm{SO}(3,1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry and a ${\mathbb{Z}}_{2}$ gauge structure. Interwire couplings induce a transition to a topologically ordered metallic state characterized by fractionalized excitations and eightfold ground state degeneracy on a torus. Our findings connect impurity-based non-Fermi-liquid behavior to lattice topological order, with potential implications for quantum materials and topological quantum computation.

arXiv:2410.01759•Physical review. B./Physical review. B•Nov 10, 2025•2 citations
Entanglement of spin and orbital Kondo effect is investigated on the basis of a Kondo-type exchange model with twofold orbital degeneracy. By using Wilson's numerical renormalization-group method, we examine dynamical and thermal properties respecting the difference in time-reversal property of multipole operators. In the presence of particle-hole symmetry, the model has a new non-Fermi-liquid fixed point with a fractional entropy. The spectral intensity of the quadrupole susceptibility diverges in the zero-frequency limit, while the dipole susceptibility shows a Fermi-liquid-like behavior. This is understood by mapping to the two-channel Kondo model, in which the dipole moment is mapped onto the operators with the scaling dimension Δm=1Δ_m=1Δm​=1, while the quadrupole moment onto the operators with another scaling dimension Δe=1/2Δ_e=1/2Δe​=1/2. Even for a fairly particle-hole asymmetric case with the Fermi-liquid ground state, the non-Fermi-liquid behavior has significant influences in electric and thermal properties.
Numerical renormalization-group results on entropy of the anisotropic two-channel Kondo model with the band-width cutoff (DDD) in the presence of a magnetic field (hhh) are obtained to determine crossover temperature from the non-Fermi liquid to Fermi liquid fixed point. It is found that the crossover temperature (TxT_{\rm x}Tx​) is given by Tx≡rTK∼D(ΔJ/Jav)2e−1/JavT_{\rm x} \equiv {r} T_{\rm K} \sim D(ΔJ/J_{\rm av})^2 e^{-1/J_{\rm av}}Tx​≡rTK​∼D(ΔJ/Jav​)2e−1/Jav​ when $(h /T_{\rm K})^2 \ll r \ll 1 $, where TKT_{\rm K}TK​, JavJ_{\rm av}Jav​ and ΔJΔJΔJ are the Kondo temperature, the average and difference of the exchange coupling constants, respectively. This result indicates that non-Fermi liquid behavior can be seen even if ΔJ>TKΔJ > T_{\rm K}ΔJ>TK​. Robust similarities of the crossover behavior in the region around the non-Fermi liquid critical point to that of the two-impurity Kondo model 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.
Using the numerical renormalization group method, we study a generalized two-channel Kondo model where the impurity has a quadrupole moment (pseudospin) and a magnetic moment (flavor). This model may be of relevance to the Ce ions in CeB6{\mathrm{CeB}}_{6}CeB6​ and the Cu ions in cuprate superconductors. We find that the nontrivial fixed point of the two-channel Kondo model is unstable against flavor exchange coupling. The system flows to a non-Fermi-liquid fixed line. In the presence of a double tensor interaction, which breaks particle-hole symmetry, the system flows to a Fermi-liquid fixed line.
We study by Wilson numerical renormalization group the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting that follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi-liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudogap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also consider the effect of several particle-hole symmetry-breaking terms. We show that particle-hole perturbations that simply shift the orbital energies do not wash out the fixed point, unlike those perturbations that hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry. In other words, the pseudogap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models that map onto this Anderson impurity model in the limit of large lattice coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality that reflects the impurity non-Fermi-liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk coherent symmetry-broken phases, which we identify for different lattice models.
We discuss the two-channel Kondo problem with a pseudogap density of states $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{|\ensuremath{\omega}|}^{r}$ of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi-liquid behavior of the metallic r=0r=0r=0 case, is replaced by a stable particle-hole-symmetric intermediate-coupling fixed point for $0<r<{r}_{\mathrm{max}}\ensuremath{\approx}0.23$. For r>rmaxr>{r}_{\mathrm{max}}r>rmax​, this non-Fermi-liquid phase disappears, and instead a critical fixed point with an emergent spin-channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose low-energy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ $\ensuremath{\epsilon}$ expansion techniques to calculate critical properties near the critical dimensions r=0r=0r=0 and 1, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.
There has been significant recent interest in the potential exotic properties of multichannel Kondo lattices and their connection to quantum materials, but the strongly coupled nature of these models has posed challenges to theoretical investigations. We study the emergence of topological order in a two-dimensional two-channel Kondo lattice (2CKL) in a time-reversal symmetry-broken channel symmetric phase using a coupled-wire construction from one-dimensional (1D) 2CKLs. Through bosonization and symmetry analysis, we show that away from particle-hole symmetry, the 1D 2CKL model flows to an infrared fixed point with an emergent $\mathrm{SO}(3,1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry and a Z2{\mathbb{Z}}_{2}Z2​ gauge structure. Interwire couplings induce a transition to a topologically ordered metallic state characterized by fractionalized excitations and eightfold ground state degeneracy on a torus. Our findings connect impurity-based non-Fermi-liquid behavior to lattice topological order, with potential implications for quantum materials and topological quantum computation.