ABSTRACT Frustration refers to the inability to satisfy competing interactions simultaneously, of... more ABSTRACT Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin liquid phase. An intrinsic effect lifting this degeneracy is entropic order-by-disorder. We present strong evidence that a classical nearest neighbor Heisenberg model on the swedenborgite lattice exhibits both an extended spin-liquid phase as well as entropic order-by-disorder choosing planar configurations after a first order transition. We argue that this observation renders magnetic insulators such as ${\rm{RBaCo}}_4{\rm{O}}_7$, where R denotes a rare earth atom, prime candidates for displaying spin liquid behavior and entropic order-by-disorder physics due to their large exchange constant.
We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb i... more We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system. We use the bosonization technique followed by the replica trick to average over the quenched randomness. An expression for the localization length of the system is then obtained using the renormalization group method and also a physical argument. We then find the density of states for different values of the energy; we get different expressions depending on whether the energy is larger than or smaller than the inverse of the localization length. We work in the limit of weak disorder where the localization length is very large; at that length scale, the LRCI has the effect of reducing the interaction parameter K of the TLL to a value much smaller than the noninteracting value of unity.
Chiral magnets, such as MnSi, display a rich finite temperature phase diagram in an applied magne... more Chiral magnets, such as MnSi, display a rich finite temperature phase diagram in an applied magnetic field. The most unusual of the phases encountered is the so called A-phase characterized by a triangular lattice of skyrmion tubes. Its existence cannot be captured within a mean-field treatment of a Landau-Ginzburg functional but thermal fluctuations to Gaussian order are required to stabilize it 1 . In this note we go beyond Gaussian order in a fully non-perturbative study of a three dimensional lattice spin model using classical Monte Carlo simulations. We demonstrate that the A-phase is indeed stabilized by thermal fluctuations and furthermore we reproduce the full phase diagram found in experiment. The thermodynamic signatures of the helimagnetic transition upon cooling from the paramagnet are qualitatively consistent with experimental findings and lend further support to the Brazovskii scenario 2 which describes a fluctuation driven first order transition due to the abundance of soft modes 3 .
We investigate Kondo physics in a host with a strongly diverging density of states. This study is... more We investigate Kondo physics in a host with a strongly diverging density of states. This study is motivated by a recent work on vacancies in the graphene honeycomb lattice, whose density of states is enhanced at low energies due to potential scattering. The generalized quantum impurity model describing the vacancy is shown to support a spin-1 2 (doublet) Kondo phase. The special role played by a diverging host density of states is examined in detail, with distinctive signatures associated with the powerlaw Kondo effect shown to appear in thermodynamic quantities and the scattering t matrix, with a strongly enhanced Kondo temperature. Although the effective Kondo model supports a novel stable phase characterized by strong renormalized particle-hole asymmetry, we find that this phase cannot in fact be accessed in the full Anderson model. In the more realistic case where the divergence in the host density of states is cut off at low energies, a crossover is generated between pristine powerlaw Kondo physics and a regular Kondo strong coupling state.
We study the thermal and electric transport of a fluid of interacting Dirac fermions as they aris... more We study the thermal and electric transport of a fluid of interacting Dirac fermions as they arise in single-layer graphene. We include Coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature T and chemical potential µ. In the critical regime µ T where both bands above and below the Dirac point contribute to transport we find pronounced deviations from Fermi liquid behavior, universal, collision-dominated values for transport coefficients and a cyclotron resonance of collective nature. In the collision-dominated high temperature regime the linear thermoelectric transport coefficients are shown to obey the constraints of relativistic magnetohydrodynamics which we derive microscopically from Boltzmann theory. The latter also allows us to describe the crossover to disorder-dominated Fermi liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields.
We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Usi... more We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Using a Boltzmann equation approach we study a variety of limits ranging from the non-degenerate interaction dominated limit close to charge neutrality all the way to the Fermi liquid regime. In the non-degenerate limit we find that the presence of the passive layer can largely influence the conductivity of the active layer despite the absence of drag. This induces a non-trivial temperature behavior of the single layer conductivity and furthermore suggests a promising strategy towards increasing the role of inelastic scattering in future experiments. For small but finite chemical potential we find that the drag resistivity varies substantially as a function of the ratio of inelastic and elastic scattering. Furthermore, we explicitly show that the clean system has a well-defined drag resistivity even though the individual conductivities diverge. We find that an extrapolation from finite chemical potential to zero chemical potential and to the clean system is delicate and the order of limits matters. While the drag resistivity ρ d extrapolates to zero upon taking the limit limα→∞ limµ a =µp→0 ρ d = 0 it has a finite value in the opposite order of limits limµ a=µp→0 limα→∞ ρ d = − 1 σ 0 (µa and µp are chemical potentials of the active and passive layer). The limiting value in the latter case is set by the interaction dominated single layer conductivity σ0 of clean graphene and in that sense is a universal number. In the Fermi liquid regime we analyze drag as a function of temperature T and the distance d between the layers and compare our results to existing theoretical and experimental results. In addition to the conventional 1/d 4 -dependence with an associated T 2 -behavior we find there is another regime of 1/d 5 -dependence where drag varies in linear-in-T fashion. The relevant parameter separating these two regimes is given by d = T d/vF (vF is the Fermi velocity), where d 1 corresponds to T 2 -behavior, while d 1 corresponds to T -behavior. We speculate that the broad crossover between these two regimes was observed in recent experiments on graphene as well as old experiments on conventional two dimensional electron gases. We close with a discussion of the role of screening and the determination of the drag resistivity as function of the charge carrier densities in the two layers under very general circumstances covering the whole crossover from the non-degenerate to the degenerate limit in both layers independently.
We present an analytic theory of quantum criticality in the quasi one-dimensional topological And... more We present an analytic theory of quantum criticality in the quasi one-dimensional topological Anderson insulators of class AIII and BDI. We describe the systems in terms of two parameters (g, χ) representing localization and topological properties, respectively. Surfaces of half-integer valued χ define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two parameter flow describing the class A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We check the quantitative validity of our theory by comparison to numerical transfer matrix computations.
Noninteracting insulating electronic states of matter can be classified according to their symmet... more Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this work we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators, but only if the Sz-component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes and the surface states localize, even if the crystalline symmetries are intact on average.
This article summarizes our understanding of the Kondo effect in graphene, primarily from a theor... more This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphene's Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we point out connections to other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids. arXiv:1208.3113v2 [cond-mat.str-el]
Recently, neutron scattering data on powder samples of Zn-paratacamite, ZnxCu4−x(OH)6Cl2, with sm... more Recently, neutron scattering data on powder samples of Zn-paratacamite, ZnxCu4−x(OH)6Cl2, with small Zn concentration has been interpreted as evidence for valence bond solid and Néel ordering . We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and X-ray scattering experiments that can test our predictions.
In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature.... more In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin de... more We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2 frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow the flow towards a stable strong-coupling state. Since the low-energy bosons live around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
The pseudogap Kondo problem, describing quantum impurities coupled to fermionic quasiparticles wi... more The pseudogap Kondo problem, describing quantum impurities coupled to fermionic quasiparticles with a pseudogap density of states, ρ(ω) ∝ |ω| r , shows a rich zero-temperature phase diagram, with different screened and free moment phases and associated transitions. We analyze both the particlehole symmetric and asymmetric cases using renormalization group techniques. In the vicinity of r = 0, which plays the role of a lower-critical dimension, an expansion in the Kondo coupling is appropriate. In contrast, r = 1 is the upper-critical dimension in the absence of particle-hole symmetry, and here insight can be gained using an expansion in the hybridization strength of the Anderson model. As a by-product, we show that the particle-hole symmetric strong-coupling fixed point for r < 1 is described by a resonant level model, and corresponds to an intermediate-coupling fixed point in the renormalization group language. Interestingly, the value r = 1/2 plays the role of a second lower-critical dimension in the particle-hole symmetric case, and there we can make progress by a novel expansion performed around a resonant level model. The different expansions allow a complete description of all critical fixed points of the models and can be used to compute a variety of properties near criticality, describing universal local-moment fluctuations at these impurity quantum phase transitions.
The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment... more The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment with a power-law density of states, displays continuous quantum phase transitions between free and screened moment phases. In this paper we employ renormalization group techniques to analytically calculate universal crossover functions, associated to these transitions, for various observables. Quantitative agreement with the results of Numerical Renormalization Group (NRG) simulations is obtained for temperature-dependent static and zero-temperature dynamic quantities, at and away from criticality. In the notoriously difficult realm of finite-temperature low-frequency dynamics, usually inaccessible to both NRG and perturbative methods, we show that progress can be made by a suitable renormalization procedure in the framework of the Callan-Symanzik equations. Our general strategy can be extended to other zero-temperature phase transitions, both in quantum impurity models and bulk systems.
We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| r , of th... more We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| 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 < rmax ≈ 0.23. For 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 lowenergy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions r = 0 and r = 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.
ABSTRACT Frustration refers to the inability to satisfy competing interactions simultaneously, of... more ABSTRACT Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin liquid phase. An intrinsic effect lifting this degeneracy is entropic order-by-disorder. We present strong evidence that a classical nearest neighbor Heisenberg model on the swedenborgite lattice exhibits both an extended spin-liquid phase as well as entropic order-by-disorder choosing planar configurations after a first order transition. We argue that this observation renders magnetic insulators such as ${\rm{RBaCo}}_4{\rm{O}}_7$, where R denotes a rare earth atom, prime candidates for displaying spin liquid behavior and entropic order-by-disorder physics due to their large exchange constant.
We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb i... more We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system. We use the bosonization technique followed by the replica trick to average over the quenched randomness. An expression for the localization length of the system is then obtained using the renormalization group method and also a physical argument. We then find the density of states for different values of the energy; we get different expressions depending on whether the energy is larger than or smaller than the inverse of the localization length. We work in the limit of weak disorder where the localization length is very large; at that length scale, the LRCI has the effect of reducing the interaction parameter K of the TLL to a value much smaller than the noninteracting value of unity.
Chiral magnets, such as MnSi, display a rich finite temperature phase diagram in an applied magne... more Chiral magnets, such as MnSi, display a rich finite temperature phase diagram in an applied magnetic field. The most unusual of the phases encountered is the so called A-phase characterized by a triangular lattice of skyrmion tubes. Its existence cannot be captured within a mean-field treatment of a Landau-Ginzburg functional but thermal fluctuations to Gaussian order are required to stabilize it 1 . In this note we go beyond Gaussian order in a fully non-perturbative study of a three dimensional lattice spin model using classical Monte Carlo simulations. We demonstrate that the A-phase is indeed stabilized by thermal fluctuations and furthermore we reproduce the full phase diagram found in experiment. The thermodynamic signatures of the helimagnetic transition upon cooling from the paramagnet are qualitatively consistent with experimental findings and lend further support to the Brazovskii scenario 2 which describes a fluctuation driven first order transition due to the abundance of soft modes 3 .
We investigate Kondo physics in a host with a strongly diverging density of states. This study is... more We investigate Kondo physics in a host with a strongly diverging density of states. This study is motivated by a recent work on vacancies in the graphene honeycomb lattice, whose density of states is enhanced at low energies due to potential scattering. The generalized quantum impurity model describing the vacancy is shown to support a spin-1 2 (doublet) Kondo phase. The special role played by a diverging host density of states is examined in detail, with distinctive signatures associated with the powerlaw Kondo effect shown to appear in thermodynamic quantities and the scattering t matrix, with a strongly enhanced Kondo temperature. Although the effective Kondo model supports a novel stable phase characterized by strong renormalized particle-hole asymmetry, we find that this phase cannot in fact be accessed in the full Anderson model. In the more realistic case where the divergence in the host density of states is cut off at low energies, a crossover is generated between pristine powerlaw Kondo physics and a regular Kondo strong coupling state.
We study the thermal and electric transport of a fluid of interacting Dirac fermions as they aris... more We study the thermal and electric transport of a fluid of interacting Dirac fermions as they arise in single-layer graphene. We include Coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature T and chemical potential µ. In the critical regime µ T where both bands above and below the Dirac point contribute to transport we find pronounced deviations from Fermi liquid behavior, universal, collision-dominated values for transport coefficients and a cyclotron resonance of collective nature. In the collision-dominated high temperature regime the linear thermoelectric transport coefficients are shown to obey the constraints of relativistic magnetohydrodynamics which we derive microscopically from Boltzmann theory. The latter also allows us to describe the crossover to disorder-dominated Fermi liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields.
We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Usi... more We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Using a Boltzmann equation approach we study a variety of limits ranging from the non-degenerate interaction dominated limit close to charge neutrality all the way to the Fermi liquid regime. In the non-degenerate limit we find that the presence of the passive layer can largely influence the conductivity of the active layer despite the absence of drag. This induces a non-trivial temperature behavior of the single layer conductivity and furthermore suggests a promising strategy towards increasing the role of inelastic scattering in future experiments. For small but finite chemical potential we find that the drag resistivity varies substantially as a function of the ratio of inelastic and elastic scattering. Furthermore, we explicitly show that the clean system has a well-defined drag resistivity even though the individual conductivities diverge. We find that an extrapolation from finite chemical potential to zero chemical potential and to the clean system is delicate and the order of limits matters. While the drag resistivity ρ d extrapolates to zero upon taking the limit limα→∞ limµ a =µp→0 ρ d = 0 it has a finite value in the opposite order of limits limµ a=µp→0 limα→∞ ρ d = − 1 σ 0 (µa and µp are chemical potentials of the active and passive layer). The limiting value in the latter case is set by the interaction dominated single layer conductivity σ0 of clean graphene and in that sense is a universal number. In the Fermi liquid regime we analyze drag as a function of temperature T and the distance d between the layers and compare our results to existing theoretical and experimental results. In addition to the conventional 1/d 4 -dependence with an associated T 2 -behavior we find there is another regime of 1/d 5 -dependence where drag varies in linear-in-T fashion. The relevant parameter separating these two regimes is given by d = T d/vF (vF is the Fermi velocity), where d 1 corresponds to T 2 -behavior, while d 1 corresponds to T -behavior. We speculate that the broad crossover between these two regimes was observed in recent experiments on graphene as well as old experiments on conventional two dimensional electron gases. We close with a discussion of the role of screening and the determination of the drag resistivity as function of the charge carrier densities in the two layers under very general circumstances covering the whole crossover from the non-degenerate to the degenerate limit in both layers independently.
We present an analytic theory of quantum criticality in the quasi one-dimensional topological And... more We present an analytic theory of quantum criticality in the quasi one-dimensional topological Anderson insulators of class AIII and BDI. We describe the systems in terms of two parameters (g, χ) representing localization and topological properties, respectively. Surfaces of half-integer valued χ define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two parameter flow describing the class A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We check the quantitative validity of our theory by comparison to numerical transfer matrix computations.
Noninteracting insulating electronic states of matter can be classified according to their symmet... more Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this work we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators, but only if the Sz-component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes and the surface states localize, even if the crystalline symmetries are intact on average.
This article summarizes our understanding of the Kondo effect in graphene, primarily from a theor... more This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphene's Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we point out connections to other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids. arXiv:1208.3113v2 [cond-mat.str-el]
Recently, neutron scattering data on powder samples of Zn-paratacamite, ZnxCu4−x(OH)6Cl2, with sm... more Recently, neutron scattering data on powder samples of Zn-paratacamite, ZnxCu4−x(OH)6Cl2, with small Zn concentration has been interpreted as evidence for valence bond solid and Néel ordering . We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and X-ray scattering experiments that can test our predictions.
In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature.... more In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin de... more We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2 frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow the flow towards a stable strong-coupling state. Since the low-energy bosons live around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
The pseudogap Kondo problem, describing quantum impurities coupled to fermionic quasiparticles wi... more The pseudogap Kondo problem, describing quantum impurities coupled to fermionic quasiparticles with a pseudogap density of states, ρ(ω) ∝ |ω| r , shows a rich zero-temperature phase diagram, with different screened and free moment phases and associated transitions. We analyze both the particlehole symmetric and asymmetric cases using renormalization group techniques. In the vicinity of r = 0, which plays the role of a lower-critical dimension, an expansion in the Kondo coupling is appropriate. In contrast, r = 1 is the upper-critical dimension in the absence of particle-hole symmetry, and here insight can be gained using an expansion in the hybridization strength of the Anderson model. As a by-product, we show that the particle-hole symmetric strong-coupling fixed point for r < 1 is described by a resonant level model, and corresponds to an intermediate-coupling fixed point in the renormalization group language. Interestingly, the value r = 1/2 plays the role of a second lower-critical dimension in the particle-hole symmetric case, and there we can make progress by a novel expansion performed around a resonant level model. The different expansions allow a complete description of all critical fixed points of the models and can be used to compute a variety of properties near criticality, describing universal local-moment fluctuations at these impurity quantum phase transitions.
The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment... more The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment with a power-law density of states, displays continuous quantum phase transitions between free and screened moment phases. In this paper we employ renormalization group techniques to analytically calculate universal crossover functions, associated to these transitions, for various observables. Quantitative agreement with the results of Numerical Renormalization Group (NRG) simulations is obtained for temperature-dependent static and zero-temperature dynamic quantities, at and away from criticality. In the notoriously difficult realm of finite-temperature low-frequency dynamics, usually inaccessible to both NRG and perturbative methods, we show that progress can be made by a suitable renormalization procedure in the framework of the Callan-Symanzik equations. Our general strategy can be extended to other zero-temperature phase transitions, both in quantum impurity models and bulk systems.
We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| r , of th... more We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| 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 < rmax ≈ 0.23. For 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 lowenergy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions r = 0 and r = 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.
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Papers by L. Fritz