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:1207.6262 · Physical Review B

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

Kazumasa Hattori, Hirokazu Tsunetsugu

Published Aug 15, 2012• 3 citations
arXivHTMLPDF

Abstract

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 $\ensuremath{-}\mathrm{Im}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Sigma}\ensuremath{\sim}|\ensuremath{\omega}|$.

DOI
10.1103/physrevb.86.054421

Related papers

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

Regular and singular Fermi-liquid fixed points in quantum impurity models

Pankaj Mehta, Natan Andrei, Piers Coleman +2 more

We show that the traditional classification of quantum inpurity models based on thermodynamics is insufficient to probe the nature of their low-energy dynamics. We propose an analysis based on scattering theory, dividing Fermi liquids into regular Fermi liquids and singular Fermi liquids. In both cases electrons at the Fermi energy scatter elastically off the impurity, but in the case of regular Fermi liquids the scattering has analytical properties in the vicinity of the Fermi energy, while for singular Fermi liquids it does not, resulting in a breakdown of Nozi\`eres' Fermi-liquid picture and singular thermodynamic behavior. Using the Bethe ansatz and numerical renormalization group, we show that the ordinary Kondo model is a regular Fermi liquid whereas the underscreened Kondo model is a a singular Fermi liquid. Conventional regular Fermi liquid behavior is reestablished in an external magnetic field $H$, but with a density of states which diverges as $1∕H$. Our results may be relevant for the recently observed field-tuned quantum criticality in heavy electron materials.

arXiv:cond-mat/0404122•Physical Review B•Jul 14, 2005•77 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

Critical points and non-Fermi liquids in the underscreened pseudogap Kondo model

Serge Florens, Matthias Vojta C

Numerical renormalization group simulations have shown that the underscreened spin-1 Kondo impurity model with power-law bath density of states (DOS) $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{r}$ possesses various intermediate-coupling fixed points, including a stable non-Fermi-liquid phase. In this paper we discuss the corresponding universal low-energy theories, obtain thermodynamic quantities and critical exponents by renormalization group analysis together with suitable $ϵ$ expansions, and compare our results with numerical data. Whereas the particle-hole symmetric critical point can be controlled at weak coupling using a simple generalization of the spin-$1∕2$ model, we show that the stable non-Fermi-liquid fixed point must be accessed near strong coupling via a mapping onto an effective ferromagnetic ${S}_{\mathrm{eff}}=1∕2$ model with singular bath DOS with exponent ${r}_{\mathrm{eff}}=\ensuremath{-}r<0$. In addition, we consider the particle-hole asymmetric critical fixed point, for which we propose a universal field theory involving the crossing between doublet and triplet levels.

arXiv:cond-mat/0506061•Physical Review B•Sep 22, 2005•7 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

Quantum Criticality and Formation of a Singular Fermi Liquid in the Attractive SU(N>2) Anderson Model

Cătălin Paşcu Moca, Razvan Chirla, Balázs Dóra +1 more

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.

arXiv:1904.08125•Physical Review Letters•Sep 26, 2019•3 citations
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/∣Tln3T∣1/|T{\mathrm{ln}}^{3}T|1/∣Tln3T∣ at low temperatures (TTT). 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−Im\ensuremathΣ\ensuremath∼∣\ensuremathω∣\ensuremath{-}\mathrm{Im}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Sigma}\ensuremath{\sim}|\ensuremath{\omega}|\ensuremath−Im\ensuremathΣ\ensuremath∼∣\ensuremathω∣.
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 show that the traditional classification of quantum inpurity models based on thermodynamics is insufficient to probe the nature of their low-energy dynamics. We propose an analysis based on scattering theory, dividing Fermi liquids into regular Fermi liquids and singular Fermi liquids. In both cases electrons at the Fermi energy scatter elastically off the impurity, but in the case of regular Fermi liquids the scattering has analytical properties in the vicinity of the Fermi energy, while for singular Fermi liquids it does not, resulting in a breakdown of Nozi\`eres' Fermi-liquid picture and singular thermodynamic behavior. Using the Bethe ansatz and numerical renormalization group, we show that the ordinary Kondo model is a regular Fermi liquid whereas the underscreened Kondo model is a a singular Fermi liquid. Conventional regular Fermi liquid behavior is reestablished in an external magnetic field HHH, but with a density of states which diverges as 1∕H1∕H1∕H. Our results may be relevant for the recently observed field-tuned quantum criticality in heavy electron materials.
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.
Numerical renormalization group simulations have shown that the underscreened spin-1 Kondo impurity model with power-law bath density of states (DOS) $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{r}$ possesses various intermediate-coupling fixed points, including a stable non-Fermi-liquid phase. In this paper we discuss the corresponding universal low-energy theories, obtain thermodynamic quantities and critical exponents by renormalization group analysis together with suitable ϵϵϵ expansions, and compare our results with numerical data. Whereas the particle-hole symmetric critical point can be controlled at weak coupling using a simple generalization of the spin-1∕21∕21∕2 model, we show that the stable non-Fermi-liquid fixed point must be accessed near strong coupling via a mapping onto an effective ferromagnetic Seff=1∕2{S}_{\mathrm{eff}}=1∕2Seff​=1∕2 model with singular bath DOS with exponent ${r}_{\mathrm{eff}}=\ensuremath{-}r<0$. In addition, we consider the particle-hole asymmetric critical fixed point, for which we propose a universal field theory involving the crossing between doublet and triplet levels.
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.
While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.