Solution of the Anderson impurity model via the functional renormalization group

Streib, Simon; Isidori, Aldo; Kopietz, Peter

doi:10.1103/physrevb.87.201107

Cited by 23 publications

(26 citation statements)

References 26 publications

(32 reference statements)

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“…The diagrammatic FL approach has been extended to orbitally degenerate versions of the Anderson model [12,[15][16][17], see also the interaction between two impurities [19], and to out of equilibrium [20], and led to the construction of the renormalized perturbation theory [2,3,21,22] (see also Ref. [23]) and its application to various extensions of the Anderson model [24][25][26]. Nozières' quasiparticle FL approach has been widely used to study non-equilibrium transport in correlated nano-structures described by the Kondo model or generalizations thereof [11, 27-31, 33, 34].…”

Section: B Anderson Model Basicsmentioning

confidence: 99%

Fermi-liquid theory for the single-impurity Anderson model

et al. 2015

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We generalize Nozières' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozières that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives w.r.t. the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the ∼ B 2 , ∼ T 2 , and ∼ V 2 terms exactly in terms of the Fermiliquid parameters. The coefficients of T 2 , V 2 and B 2 are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

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Section: B Anderson Model Basicsmentioning

confidence: 99%

Fermi-liquid theory for the single-impurity Anderson model

et al. 2015

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“…[4,6,14]. all diagrams of plain perturbation theory [30,31,11]. Therefore, the relation between approximate 1PI fRG schemes and so-called conserving approximations [32,33] remains elusive.…”

Section: Introductionmentioning

confidence: 99%

Two-particle irreducible functional renormalization group schemes—a comparative study

Rentrop

Jakobs

Meden³

2015

J. Phys. A: Math. Theor.

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Abstract.We derive functional renormalization group schemes for Fermi systems which are based on the two-particle irreducible approach to the quantum many-body problem. In a first step, the cutoff is introduced in the non-interacting propagator as it is commonly done in functional renormalization group based on one-particle irreducible vertex functions. The most natural truncation of the resulting infinite hierarchy of flow equations is shown to be fully equivalent to self-consistent perturbation theory. An earlier suggested alternative truncation strategy is considered as well. In a second step, the cutoff is introduced in the twoparticle interaction. Again two truncation procedures are investigated, one of which was derived before. In the latter, the mean-field solution of the manybody problem is considered as the starting point of the renormalization group flow. We compare the performance and the required numerical resources for solving the coupled flow equations for all the approximate schemes by applying them to the problem of the quantum anharmonic oscillator. In a functional integral representation, this model has a formal similarity to the quantum manybody problem. The perspectives for applying the derived two-particle irreducible functional renormalization group approaches to zero-and one-dimensional systems of correlated fermions are discussed.arXiv:1501.00800v3 [cond-mat.str-el]

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“…Many other studies [13][14][15][16][17] improved the functional RG approach recently but did not capture the strong coupling regime. Only in 2013, Streib and co-workers succeeded 18 exploiting a magnetic field as regulatory cutoff and conserved Ward identities similar to a renormalized perturbation theory developed by Hewson and his co-workers [19][20][21] . The difficulties that these intricate approaches had to face underlines impressively that the Kondo effect in the Anderson impurity problem represents a true challenge.…”

Section: Summary a Conclusionmentioning

confidence: 99%

“…While the successes in the regime of small to intermediate couplings were very interesting, the strong coupling regime eluded a description by functional RG. Only recently, Streib and co-workers provided a functional RG approach with the correct strongcoupling approach 18 . The additional key element in their study is to use a large magnetic field as flow parameter which is gradually lowered to zero.…”

Section: Introductionmentioning

confidence: 99%

Effective models for Anderson impurity and Kondo problems from continuous unitary transformations

Krones

Uhrig

2015

Phys. Rev. B

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The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature TK . We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small finite parameters at arbitrarily small energies. The ground state corresponds to a bound singlet with a binding energy given by the Kondo temperature TK .

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Solution of the Anderson impurity model via the functional renormalization group

Cited by 23 publications

References 26 publications

Fermi-liquid theory for the single-impurity Anderson model

Fermi-liquid theory for the single-impurity Anderson model

Two-particle irreducible functional renormalization group schemes—a comparative study

Effective models for Anderson impurity and Kondo problems from continuous unitary transformations

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