arXiv subjects

A. C. Hewson

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

At least 37 records · Page 2Linked to original sources

arXiv2007

Field dependent quasiparticles in a strongly correlated local system II

We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field $H$, developed in earlier work, to the non-symmetric model. The renormalized parameters are deduced from the low energy NRG fixed point for arbitrary field values. We find quasiparticle resonance widths, $\tildeΔ_σ(H)$, which depend in general on the spin $σ$ as well as $H$. The low temperature static properties can be expressed completely in terms of these parameters, which can also be used as inputs for a renormalized perturbation theory. We show that taking into account repeated quasiparticle scattering gives results for the longitudinal and transverse dynamic spin susceptibilities which are in very good agreement with those obtained from direct NRG calculations.

cond-mat.str-el↗

arXiv2006

NRG approach to the transport through a finite Hubbard chain connected to reservoirs

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.

cond-mat.mes-hall↗

arXiv2005

Spin and Charge Dynamics in a Renormalised Perturbation Theory

We calculate the spin and charge dynamical susceptibilities of a strongly correlated impurity model in a renormalised perturbation theory. The irreducible for vertices for the quasiparticle scattering are deduced from the renormalised parameters, which have been calculated by fitting of the low-lying levels of a numerical renormalisation group (NRG) calculation to those of an effective Anderson model. The susceptibilities are asymptotically exact in the low frequency limit and satisfy the Korringa-Shiba relation. By comparing the results with those calculated from a direct NRG calculation, we show that the renormalised perturbation theory (RPT) description gives a very good description of spin dynamics for all values of the local interaction U, not only at low frequencies but over the whole relevant frequency range. In the presence of a magnetic field the approach can be generalised using field dependent renormalised parameters to calculate the transverse and parallel spin dynamic susceptibilities. The RPT results give accurate results for the spin dynamics over the whole frequency range and for all values of the magnetic field.

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arXiv2005

Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field

We derive an exact expression for the differential conductance for a quantum dot in an arbitrary magnetic field for small bias voltage. The derivation is based on the symmetric Anderson model using renormalized perturbation theory and is valid for all values of the on-site interaction $U$ including the Kondo regime. We calculate the critical magnetic field for the splitting of the Kondo resonance to be seen in the differential conductivity as function of bias voltage. Our calculations for small field show that the peak position of the component resonances in the differential conductance are reduced substantially from estimates using the equilibrium Green's function. We conclude that it is important to take the voltage dependence of the local retarded Green's function into account in interpreting experimental results

cond-mat.str-el↗

arXiv2005

Magnetic Field Effects on Quasiparticles in Strongly Correlated Local Systems

We show that quasiparticles in a magnetic field of arbitrary strength $H$ can be described by field dependent parameters. We illustrate this approach in the case of an Anderson impurity model and use the numerical renormalization group (NRG) to calculate the renormalized parameters for the levels with spin $σ$, $\tildeε_{\mathrm{d},σ}(H)$, resonance width $\tildeΔ(H)$ and the effective local quasiparticle interaction $\tilde U(H)$. In the Kondo or strong correlation limit of the model the progressive de-renormalization of the quasiparticles can be followed as the magnetic field is increased. The low temperature behaviour, including the conductivity, in arbitrary magnetic field can be calculated in terms of the field dependent parameters using the renormalized perturbation expansion. Using the NRG the field dependence of the spectral density on higher scales is also calculated.

cond-mat.str-el↗

arXiv2005

Polaronic Quasiparticles in a Strongly Correlated Electron Band

We show that a strongly renormalized band of polaronic quasiparticle excitations is induced at the Fermi level of an interacting many-electron system on increasing the coupling of the electrons to local phonons. We give results for the local density of states at zero temperature both for the electrons and phonons. The polaronic quasiparticles satisfy Luttinger's theorem for all regimes considered, and their dispersion shows a kink similar to that observed experimentally in copper oxides. We calculate the quasiparticle weight factor $z$ and deduce the local effective inter-quasiparticle interaction $\tilde U$. Our calculations are based on the dynamical mean field theory and the numerical renormalization group for the hole-doped Holstein-Hubbard model and large on-site repulsion.

cond-mat.str-el↗

arXiv2005

Determination of the phase shifts for interacting electrons connected to reservoirs

We describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case.

cond-mat.mes-hall↗

arXiv2004

Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps $Δ_α=|Δ_α| e^{i θ_α}$, where $α= L, R$ for the lead at left and right. We show that, when one of the SC gaps is much larger than the others $|Δ_L| \gg |Δ_R|$, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of $Δ_R$ and the Anderson impurity with an extra onsite SC gap of $Δ_d \equiv Γ_L e^{i θ_L}$. Here $θ_L$ and $Γ_L$ are defined with respect to the starting model, and $Γ_L$ is the level width due to the coupling with the left lead. Based on this simplified model, we study the ground-state properties for the asymmetric gap, $|Δ_L| \gg |Δ_R|$, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps $ϕ\equiv θ_R -θ_L$, which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.

cond-mat.mes-hall↗

arXiv2004

The Strong Coupling Fixed-Point Revisited

In recent work we have shown that the Fermi liquid aspects of the strong coupling fixed point of the s-d and Anderson models can brought out more clearly by interpreting the fixed point as a renormalized Anderson model, characterized by a renormalized level $\tildeε_d$, resonance width, $\tildeΔ$, and interaction $\tilde U$, and a simple prescription for their calculation was given using the numerical renormalization group (NRG). These three parameters completely specify a renormalized perturbation theory (RPT) which leads to exact expressions for the low temperature behaviour. Using a combination of the two techniques, NRG to determine $\tildeε_d$, $\tildeΔ$, and $\tilde U$, and then substituting these in the RPT expressions gives a very efficient and accurate way of calculating the low temperature behaviour of the impurity as it avoids the necessity of subtracting out the conduction electron component. Here we extend this approach to an Anderson model in a magnetic field, so that $\tildeε_d$, $\tildeΔ$, and $\tilde U$ become dependent on the magnetic field. The de-renormalization of the renormalized quasiparticles can then be followed as the magnetic field strength is increased. Using these running coupling constants in a RPT calculation we derive an expression for the low temperature conductivity for arbitrary magnetic field strength.

cond-mat.str-el↗

arXiv2004

Phase diagram and dynamic response functions of the Holstein-Hubbard model

We present the phase diagram and dynamical correlation functions for the Holstein-Hubbard model at half filling and at zero temperature. The calculations are based on the Dynamical Mean Field Theory. The effective impurity model is solved using Exact Diagonalization and the Numerical Renormalization Group. Excluding long-range order, we find three different paramagnetic phases, metallic, bipolaronic and Mott insulating, depending on the Hubbard interaction U and the electron-phonon coupling g. We present the behaviour of the one-electron spectral functions and phonon spectra close to the metal insulator transitions.

cond-mat.str-el↗

arXiv2004

Renormalized Parameters for Impurity Models

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tildeε_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.

cond-mat.str-el↗

arXiv2004

Dynamic response functions for the Holstein-Hubbard model

We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propagator shows a characteristic softening near the metal to bipolaronic transition but there is very little softening on the approach to the Mott transition.

cond-mat.str-el↗

arXiv2004

First- and Second Order Phase Transitions in the Holstein-Hubbard Model

We investigate metal-insulator transitions in the Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U. We also present results for the quasiparticle weight and the double-occupancy as function of U and g.

cond-mat.str-el↗

arXiv2002

Gap formation and soft phonon mode in the Holstein model

We investigate electron-phonon coupling in many-electron systems using dynamical mean-field theory in combination with the numerical renormalization group. This non-perturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.

cond-mat.str-el↗

arXiv2001

Renormalized perturbation calculations for the single impurity Anderson model

We illustrate the renormalized perturbation expansion method by applying it to a single impurity Anderson model. Previously, we have shown that this approach gives the {\it exact} leading order results for the specific heat, spin and charge susceptibilities and leading order temperature dependence of the resistivity for this model in the Fermi-liquid regime, when carried out to second order in the renormalized interaction $\tilde U$. Here we consider the effects of higher order quasi-particle scattering and calculate the third order contributions to the $H^3$ term in the impurity magnetization for the symmetric model in a weak magnetic field $H$. The result is asymptotically exact in the weak coupling regime, and is very close to the exact Bethe ansatz result in the Kondo regime. We also calculate the quasi-particle density of states in a magnetic field, which is of interest in relation to recent experimental work on quantum dots.

cond-mat.str-el↗

arXiv2001

Critical behaviour near the metal-insulator transition of a doped Mott insulator

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for $U$ larger than a critical value $U_c$, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping.

cond-mat.str-el↗

arXiv2001

Phase diagram of the Mott Transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the $d$-orbital, the charge-transfer energy between the $d$- and $p$-orbitals and the hopping integrals between $p-d$, $d-d$ and $p-p$ orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method.

cond-mat.str-el↗

arXiv1999

Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.

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