arXiv subjects

A. C. Hewson

Publications and source records attributed to A. C. Hewson.

At least 19 recordsLinked to original sources

arXiv2020

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling III: non-equilibrium transport

We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys.\ Rev.\ B {\bf 64}, 153305 (2001)] to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and anti-symmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order $T^2$ and $(eV)^2$ are determined at low temperatures $T$ and low bias voltages $eV$. Away from half-filling, these corrections can be expressed in terms of the linear and non-linear static susceptibilities which represent the two-body and three-body fluctuations, respectively. We calculate the non-linear susceptibilities using the numerical renormalization group, to explore the differential conductance $dI/dV$ through a quantum dot. We find that the two-body fluctuations dominate the corrections in the Kondo regime at zero magnetic field. The contribution of the three-body fluctuations become significant far away from half-filling, especially in the valence-fluctuation regime and empty-orbital regimes. In finite magnetic fields, the three-body contributions become comparable to the two-body contributions, and play an essential role in the splitting of the zero-bias conductance peak occurring at a magnetic field of the order of the Kondo energy scale. We also apply our microscopic formulation to the magneto-resistance and thermal conductivity of dilute magnetic alloys away from half-filling.

cond-mat.mes-hall↗

arXiv2020

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling II: equilibrium properties

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half-filling for finite magnetic fields, using the Ward identities with careful consideration of the anti-symmetry and analytic properties. The asymptotic form of the vertex function $Γ_{σσ';σ'σ}^{}(iω,iω';iω',iω)$ is determined up to terms of linear order with respect to the two frequencies $ω$ and $ω'$, as well as the $ω^2$ contribution for anti-parallel spins $σ'\neq σ$ at $ω'=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida. The $ω^2$ real part of the self-energy $Σ_σ^{}(iω)$ is shown to be expressed in terms of the double derivative $\partial^2Σ_σ^{}(0)/\partial ε_{dσ}^{2}$ with respect to the impurity energy level $ε_{dσ}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora in the Nozières phenomenological Fermi-liquid theory [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy, and find that the real part can be expressed in terms of the three-body correlation function $χ_{\uparrow\downarrow,-σ}^{[3]} = \partial χ_{\uparrow\downarrow}/\partial ε_{d,-σ}^{}$. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function $Γ_{σσ;σσ}^{}(iω,0;0,iω)$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $ω$ vanish as a result of the cancellation of four related Feynman diagrams which are related to each other through the anti-symmetry operation.

cond-mat.str-el↗

arXiv2018

Magnetic field induced quantum criticality and the Luttinger sum rule

We show that when there is a sudden transition from a small to a large Fermi surface at a field-induced quantum critical point, similar to what may have been observed in some heavy-fermion compounds, an additional term has to be taken into account in the Luttinger-Friedel sum rule.We calculate this additional term for a local model which has a field-induced quantum critical point (QCP) and show that it changes abruptly at the transition, such that it satisfies a generalized Luttinger-Friedel sum rule on each side of the transition, and characterizes the two Fermi-liquid phases separated by the QCP as a discrete (topological) index.

cond-mat.str-el↗

arXiv2018

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling

We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada-Yosida. It includes partly a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. In our formulation, the Fermi-liquid parameters such as the quasi-particle energy, damping, and transport coefficients are related to each other through the total vertex $Γ_{σσ';σ'σ} (ω, ω'; ω', ω)$, which may be regarded as a generalized Landau quasi-particle interaction. We obtain exactly this function up to linear order with respect to the frequencies $ω$ and $ω'$ using the anti-symmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half-filling through the non-linear susceptibilities. We also apply the formulation to non-equilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

cond-mat.mes-hall↗

arXiv2017

Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of $I_{\rm L}$ with $I_{\rm L}=\pmπ/2$, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids. Here we show the same values, $I_{\rm L}=\pmπ/2$, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.

cond-mat.str-el↗

arXiv2016

Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model

We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low energy Fermi liquid fixed point using the results of a numerical renormalization group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low density limit there is significant renormalization of the local quasiparticle interaction $\tilde U$, in agreement with estimates based on the two-particle scattering theory of Kanamori (1963). On the approach to the Mott transition we find a finite ratio for $\tilde U/\tilde D$, where $2\tilde D$ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction $U$ or on increasing the density to half-filling.The leading $ω^2$ term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. The dynamic ${\bf q},ω$ spin susceptibility $χ({\bf q},ω)$ is also estimated from repeated quasiparticle scattering with a local renormalized scattering vertex.

cond-mat.str-el↗

arXiv2013

Renormalized perturbation theory and scaling for an impurity Anderson model

We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized parameters to scale from a weak correlation to a strong correlation regime. We show that, using simple approximation schemes in different parameter regimes, remarkably accurate results can be obtained for all magnetic field values by comparing the results with those from direct numerical renormalization group and Bethe ansatz calculations.

cond-mat.str-el↗

arXiv2012

Study of Hund's rule coupling in models of magnetic impurities and quantum dots

Studies of the effects of the Hund's rule coupling J_H in multiple orbit impurities or quantum dots using different models have led to quite different predictions for the Kondo temperature T_K as a function of J_H. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization group (NRG) calculations, we deduce the renormalized parameters for the Fermi liquid regime, and show that, despite the differences between the models, the low energy fixed point in the strong correlation regime is universal with a single energy scale T_K, and just two renormalized interaction parameters, a renormalized single orbital term, U = 4T_K, and renormalized Hund's rule term, J_H = 8T_K/3.

cond-mat.str-el↗

arXiv2012

Phase diagram and critical points of a double quantum dot

We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct interaction $U_{12}$ and an exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.

cond-mat.str-el↗

arXiv2011

Convergence of energy scales on the approach to a local quantum critical point

We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two impurity Anderson model. The two impurities are coupled by an inter-impurity exchange interaction $J$ and direct interaction $U_{12}$ and are hybridized with separate conduction channels.The low energy behavior is described in terms of renormalized parameters, which can be deduced from numerical renormalization group (NRG) calculations. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor $z\to 0$, and the renormalized parameters can be expressed in terms of a single energy scale $T^*$. The values of the renormalized interaction parameters in terms of $T^*$ can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation as they are greater than or equal to the effective band width. These predictions are confirmed by the NRG calculations, including the case when the onsite interaction U=0.

cond-mat.str-el↗

arXiv2011

Kondo effects in a triangular triple quantum dot with lower symmetries

The triangular triple quantum dot is an interesting system which can demonstrate various types of the Kondo effects, such as the one due to the local spin S=1 moment caused by the Nagaoka ferromagnetic mechanism and the SU(4) Kondo effect. We theoretically study the low-temperature properties and the Kondo energy scale of the triangular triple quantum dot, using the Wilson numerical renormalization group. We have explored a wide parameter region of the electron-filling and distortions which break the symmetry of an equilateral structure. Our results give a comprehensive overview of how the Kondo behavior varies in the different the regions in the wide parameter space of the triangular triple quantum dot.

cond-mat.mes-hall↗

arXiv2011

Transport Coefficients of the Anderson Model

The transport coefficients of the Anderson model require knowledge of both the temperature and frequency dependence of the single--particle spectral densities and consequently have proven difficult quantities to calculate. Here we show how these quantities can be calculated via an extension of Wilson's numerical renormalization group method. Accurate results are obtained in all parameter regimes and for the full range of temperatures of interest ranging from the high temperature perturbative regime $T>>T_{K}$, through the cross--over region $T\approx T_{K}$, and into the low temperature strong coupling regime $T<<T_{K}$. The Fermi liquid relations for the $T^2$ coefficient of the resistivity and the linear coefficient of the thermopower are satisfied to a high degree of accuracy. The techniques used here provide a new highly accurate approach to strongly correlated electrons in high dimensions.

cond-mat.str-el↗

arXiv2009

Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model

We present a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. We study the evolution of the single-particle spectra throughout the crossover regime. Although the DMFT does not include the interaction of the fermions with the Goldstone mode, we find strong deviations from the mean-field theory in the intermediate and strong coupling (BEC) regimes. In particular, we show that low-energy charge fluctuations induce a transfer of spectral weight from the Bogoliubov quasiparticles to a higher-energy incoherent hump.

cond-mat.supr-con↗

arXiv2009

Gate-voltage dependence of Kondo effect in a triangular quantum dot

We study the conductance through a triangular triple quantum dot, which are connected to two noninteracting leads, using the numerical renormalization group (NRG). It is found that the system shows a variety of Kondo effects depending on the filling of the triangle. The SU(4) Kondo effect occurs at half-filling, and a sharp conductance dip due to a phase lapse appears in the gate-voltage dependence. Furthermore, when four electrons occupy the three sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism, is induced along the triangle. The temperature dependence of the entropy and spin susceptibility of the triangle shows that this moment is screened by the conduction electrons via two separate stages at different temperatures. The two-terminal and four-terminal conductances show a clear difference at the gate voltages, where the SU(4) or the S=1 Kondo effects occurring.

cond-mat.mes-hall↗

arXiv2009

Quasiparticle excitations and dynamic susceptibilities in the BCS-BEC crossover

We study dynamic ground state properties in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. Our approach is based on the attractive Hubbard model which is analyzed by the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). We present an extension of the NRG method for effective impurity models to selfconsistent calculations with superconducting symmetry breaking. In the one particle spectra we show quantitatively how the Bogoliubov quasiparticles at weak coupling become suppressed at intermediate coupling. We also present results for the spin and charge gap. The extension of the NRG method to selfconsistent superconducting solutions opens the possibility to study a range of other important applications.

cond-mat.supr-con↗

arXiv2007

Kondo effect in asymmetric Josephson couplings through a quantum dot

Asymmetry in the Josephson couplings between two superconductors through a quantum dot is studied based on a single impurity Anderson model using the numerical renormalization group (NRG). Specifically, we examine how the difference between the couplings Γ_L and Γ_R affects the ground state, which is known to show a quantum phase transition between a nonmagnetic singlet and a magnetic doublet depending on the various parameters; the Coulomb interaction U, onsite potential ε_d, level width Γ_L, Γ_R, caused by the hybridization, and superconducting gaps Δ_L and Δ_R for the leads on the left and right. Our results show that whether the local moment is fully screened or not depends substantially on the asymmetry in the couplings Γ_L \neq Γ_R. It tends to make the singlet ground state stable, while the size and phase difference of the two superconducting gaps tend to suppress the screening. We also discuss some general symmetry properties of the system and their relation to the current conservation.

cond-mat.mes-hall↗

arXiv2007

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity. They are found to be in good agreement. We show that the main low energy features of the $\bf k$-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.

cond-mat.str-el↗

arXiv2007

Field dependent quasiparticles in the infinite dimensional Hubbard model

We present dynamical mean field theory (DMFT) results for the local spectral densities of the one- and two-particle response functions for the infinite dimensional Hubbard model in a magnetic field. We look at the different regimes corresponding to half-filling, near half-filling and well away from half-filling, for intermediate and strong values of the local interaction $U$. The low energy results are analyzed in terms of quasiparticles with field dependent parameters. The renormalized parameters are determined by two different methods, both based on numerical renormalization group (NRG) calculations, and we find good agreement. Away from half-filling the quasiparticle weights, $z_σ(H)$, differ according to the spin type $σ=\uparrow$ or $σ=\downarrow$. Using the renormalized parameters, we show that DMFT-NRG results for the local longitudinal and transverse dynamic spin susceptibilities in an arbitrary field can be understood in terms of repeated scattering of these quasiparticles. We also check Luttinger's theorem for the Hubbard model and find it to be satisfied in all parameter regimes and for all values of the magnetic field.

cond-mat.str-el↗