Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry

Linneweber, Thorben; Bünemann, Jörg; Mahmoud, Zakaria M. M.; Gebhard, Florian

doi:10.1088/1361-648x/aa89d1

Cited by 4 publications

(11 citation statements)

References 42 publications

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“…The Bethe Ansatz provides the impurity-induced magnetization of the system m ii (J BA K , B, T ) at finite temperatures T and finite external fields B, see eq. (19). For small couplings, J K ≪ 1, the impurity-induced susceptibility is exponentially large, see eq.…”

Section: Impurity-induced Magnetizationmentioning

confidence: 97%

Symmetric single-impurity Kondo model on a tight-binding chain: Comparison of analytical and numerical ground-state approaches

et al. 2020

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We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurityinduced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model (SIKM) on a tight-binding chain with bandwidth W = 2D where a spin-1/2 impurity at the chain center interacts with coupling strength JK with the local spin of the bath electrons. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact extrapolations obtained from the Density-Matrix Renormalization Group (DMRG) method and from the Numerical Renormalization Group (NRG) method performed with respect the inverse system size and Wilson parameter, respectively. In contrast to the Lanczos and Yosida wave functions, the Gutzwiller variational approach becomes exact in the strong-coupling limit, JK ≫ W , and reproduces the ground-state properties from DMRG and NRG for large couplings, JK W , with a high accuracy. For weak coupling, the Gutzwiller wave function describes a symmetry-broken state with an oriented local moment, in contrast to the exact solution. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally or only locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about 10 3 sites are large enough to describe the susceptibilities down to JK/D ≈ 0.5. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states ρ0(ǫ). To compare with results from Bethe Ansatz that become exact in the wideband limit, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach χ0(JK ≪ D)/(gµB) 2 ≈ exp[1/(ρ0(0)JK)]/(2CD πeρ0(0)JK), where ln(C) is the regularized first inverse moment of the density of states. Using NRG, we determine the universal sub-leading corrections up to second order in ρ0(0)JK.

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Section: Impurity-induced Magnetizationmentioning

confidence: 97%

Symmetric single-impurity Kondo model on a tight-binding chain: Comparison of analytical and numerical ground-state approaches

et al. 2020

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“…(E.1) and (E.5) in Ref. [41]. Using Mathematica 42 we find for the semi-elliptic density of states using d 0 = ρ 0 (0) = 4/π and ln(e) = 1…”

Section: A Ground-state Energymentioning

confidence: 87%

“…(E.1) and (E.5) by Linneweber and collaborators. 41 Using Mathematica 42 we find in one dimension using d 0 = ρ 0 (0) = 2/π and ln(e) = 1…”

Section: Limit Of Small Hybridizationmentioning

confidence: 99%

Ground-state properties of the symmetric single-impurity Anderson model on a ring from density-matrix renormalization group, Hartree-Fock, and Gutzwiller theory

et al. 2019

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We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width W , the impurity interaction strength U , and the local hybridization V . We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe-Ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.

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“…In the TIAM, the Kondo coupling J K is related to the ratio of the Coulomb interaction U and the coupling strength Γ 0 . Linneweber et al investigated the TIAM on the threedimensional simple cubic lattice via a Gutzwiller variational approach and found such a QCP at a critical U c provided the impurities are placed on the lattice sites [78]. The authors indicated that their QCP is probably an artifact of the Gutzwiller variational approach: the Gutzwiller trial wave function only includes local correlations on the impurity site while the NRG reveals already for the Kondo problem the extended nature of the correlated singlet [59,60].…”

Section: Afm Rkky Coupling -The Doniach Scenariomentioning

confidence: 99%

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

2018

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We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.

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Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry

Cited by 4 publications

References 42 publications

Symmetric single-impurity Kondo model on a tight-binding chain: Comparison of analytical and numerical ground-state approaches

Symmetric single-impurity Kondo model on a tight-binding chain: Comparison of analytical and numerical ground-state approaches

Ground-state properties of the symmetric single-impurity Anderson model on a ring from density-matrix renormalization group, Hartree-Fock, and Gutzwiller theory

Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality

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