At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

Filippone, Michele; Moca, Cătălin Paşcu; Delft, Jan von; Mora, Christophe

doi:10.1103/physrevb.95.165404

Cited by 19 publications

(45 citation statements)

References 106 publications

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“…We determine the differential conductance G = dI/dV from the steady current I(V )obtained by taking time average [39,43,44,47]. Applying a magnetic field h z , we confirm the quadratic behavior G 0 (1 − c B (h z /T K ) 2 ) with the correct coefficient c B = π 2 /16 at low field and the logarithmic behavior π 2 G 0 /(16 ln 2 (h z /T K )) at high field, where G 0 is the conductance at the zero field [21,[96][97][98][99][100][101][102][103][104] (Fig. 4a).…”

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confidence: 73%

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

et al. 2018

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A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical transformation that completely decouples the impurity and bath degrees of freedom. Combining it with Gaussian states, we present a family of many-body states to efficiently encode nontrivial impurity-bath correlations. We demonstrate its successful application to the anisotropic and two-lead Kondo models by studying their spatiotemporal dynamics and universal behavior in the correlations, relaxation times, and the differential conductance. We compare them to previous analytical and numerical results. In particular, we apply our method to study new types of nonequilibrium phenomena that have not been studied by other methods, such as long-time crossover in the ferromagnetic easy-plane Kondo model. The present approach will be applicable to a variety of unsolved problems in solid-state and ultracold-atomic systems.

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confidence: 73%

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

et al. 2018

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“…Our result for the ω 2 real part, Re ∂ 2 Σ σ (iω)/∂(iω) 2 ω=0 = ∂ 2 Σ σ (0)/∂ǫ 2 dσ , reproduces exactly the FMvDM's formula. 15 We will give a more detailed comparison in a separate paper, i.e., paper III. 17 In paper III, we will also present an extension of the microscopic description to the non-equilibrium steady state driven by the bias voltage eV using the Keldysh formalism.…”

Section: Discussionmentioning

confidence: 99%

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

Oguri

Hewson

2018

Phys. Rev. B

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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 ′ = σ at ω ′ = 0. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida [Prog. Theor. Phys. 54, 316 (1975)]. The ω 2 real part of the self-energy Σ σ (iω) is shown to be expressed in terms of the double derivative ∂ 2 Σ σ (0)/∂ǫ 2 dσ with respect to the impurity energy level ǫ dσ , and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora (FMvDM) in the Nozières phenomenological Fermi-liquid theory [Phys. Rev. B 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 ↑↓ /∂ǫ d,−σ , where χ ↑↓ is the static susceptibility between anti-parallel spins. 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.

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“…It has been known that the conductance can exhibit the universal scaling behavior against external parameters such as the magnetic field, bias potential and temperature [27,[140][141][142][143][144][145][146][147][148].…”

Section: Conductance At Finite Bias and Magnetic Fieldmentioning

confidence: 99%

Variational principle for quantum impurity systems in and out of equilibrium: Application to Kondo problems

et al. 2018

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We provide a detailed formulation of the recently proposed variational approach [Y. Ashida et al., Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas by Tomonaga, Lee, Low, and Pines, we construct a canonical transformation that completely decouples the impurity from the bath degrees of freedom. By combining this transformation with a Gaussian ansatz for the fermionic bath, we obtain a family of variational many-body states that can efficiently encode the strong entanglement between the impurity and fermions of the bath. We give a detailed derivation of equations of motions in the imaginary-and real-time evolutions on the variational manifold. We benchmark our approach by applying it to investigate ground-state and dynamical properties of the anisotropic Kondo model and compare results with those obtained using matrix-product state (MPS) ansatz. We show that our approach can achieve an accuracy comparable to MPS-based methods with several orders of magnitude fewer variational parameters than the corresponding MPS ansatz. Comparisons to the Yosida ansatz and the exact solution from the Bethe ansatz are also discussed. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the conductance behavior at finite bias and magnetic fields. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point. * ashida@cat.phys.s.u-tokyo.ac.jp † tshi@itp.ac.cn wherex is the position operator of the impurity andP b is the total momentum operator of bath phonons. After employing the transformation, the conserved quantity becomes the momentum operatorp of the impurity as inferred from the relation:Û † LLP (p +P b )Û LLP =p.(2) arXiv:1802.03861v3 [cond-mat.str-el]

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At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

Cited by 19 publications

References 106 publications

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

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

Variational principle for quantum impurity systems in and out of equilibrium: Application to Kondo problems

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