Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point

Bolech, C. J.; Shah, Nayana

doi:10.1103/physrevb.93.085441

Cited by 15 publications

(12 citation statements)

References 74 publications

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“…These include the appearance of the peak in the differential conductance around h z ∼ V and the asymmetry between the conductance behavior at V = 0 with varying h z and the one at h z = 0 with varying V . In particular, it has been argued that this asymmetry is an important feature which is absent in the "conventional" bosonization treatment [110]. Yet, there seem to be differences between the asymmetric behavior found in our results and that found in the above reference.…”

Section: Conductance At Finite Bias and Magnetic Fieldcontrasting

confidence: 90%

“…We analyze out-of-equilibrium dynamics and transport properties in the two-lead Kondo model and demonstrate that our approach can be used to compute the long-time spatiotemporal dynamics and the conductance at finite bias and magnetic field. The obtained results are consistent with the previous studies in the Anderson model [88,99,114] and the exact solutions at the Toulouse point [110].…”

Section: Introductionsupporting

confidence: 93%

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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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Section: Conductance At Finite Bias and Magnetic Fieldcontrasting

confidence: 90%

Section: Introductionsupporting

confidence: 93%

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

et al. 2018

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“…The tunneling across the classically forbidden region is modeled by a tight-binding matrix overlap γt that can be taken to be energy independent in certain cases (in particular, the characteristic energy scale of dependence of the transmission coefficient, |γt| 2 , has to be much larger than both eV and kBT [8]). Here we assume that the barrier region does not allow for internal states; a situation when that happens will be discussed elsewhere [16].…”

Section: A Setting Of the Problem And Direct Solutionmentioning

confidence: 99%

“…In the future we will look at more involved examples of greater physical significance. We already started to reexamine some salient cases, and in the next paper we shall focus on the important case of transport through quantum impurities in Fermi liquids [16].…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle

Shah

Bolech

2016

Phys. Rev. B

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We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.

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“…Specifically, exact solutions [13][14][15][16][17][18] at the Toulouse point of nonequilibrium Kondo models are inapplicable to the more microscopic Anderson model. Quantum Monte Carlo [19][20][21][22] and master equation [23][24][25][26][27] methods cannot access the strong-coupling Kondo limit at zero temperature.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

2018

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We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction U is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly-correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing negative-U charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. 8, 395 (2017)].

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Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point

Cited by 15 publications

References 74 publications

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

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

Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle

Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

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