At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model
Abstract
This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. In this study, we extend a recently developed Fermi liquid (FL) theory for the asymmetric singleimpurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's lowlying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective lowenergy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spindependent groundstate occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, c _{A}, describing its leading ~ε ^{2} term, and the transport coefficients c _{V} and c _{T}, describing the leading ~V ^{2} and ~T ^{2} terms in the nonlinear differential conductance. A sign change in c _{A} or c _{V} is indicative of amore »
 Authors:

 Freie Universität Berlin (Germany). Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik; University of Geneva (Switzerland). Department of Quantum Matter Physics
 Budapest University of Technology and Economics (Hungary). BMEMTA Exotic Quantum Phase Group, Institute of Physics; University of Oradea (Romania). Department of Physics
 Brookhaven National Lab. (BNL), Upton, NY (United States). CM PMS Division; LudwigMaximiliansUniversität München (Germany). Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience
 LudwigMaximiliansUniversität München (Germany). Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience
 PSL Research University, CNRS, Université Pierre et Marie Curie, Sorbonne Universités, Université Paris Diderot (France). Laboratoire Pierre Aigrain, École normale supérieure
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1473650
 Report Number(s):
 BNL2090522018JAAM
Journal ID: ISSN 24699950; PRBMDO
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 98; Journal Issue: 7; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, and Mora, Christophe. At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.98.075404.
Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, & Mora, Christophe. At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model. United States. doi:10.1103/PhysRevB.98.075404.
Filippone, Michele, Moca, Cătălin Paşcu, Weichselbaum, Andreas, von Delft, Jan, and Mora, Christophe. Mon .
"At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model". United States. doi:10.1103/PhysRevB.98.075404. https://www.osti.gov/servlets/purl/1473650.
@article{osti_1473650,
title = {At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model},
author = {Filippone, Michele and Moca, Cătălin Paşcu and Weichselbaum, Andreas and von Delft, Jan and Mora, Christophe},
abstractNote = {This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. In this study, we extend a recently developed Fermi liquid (FL) theory for the asymmetric singleimpurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's lowlying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective lowenergy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spindependent groundstate occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, cA, describing its leading ~ε2 term, and the transport coefficients cV and cT, describing the leading ~V2 and ~T2 terms in the nonlinear differential conductance. A sign change in cA or cV is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. In conclusion, we find that the fields BA, BT, and BV at which cA, cT, and cV change sign, respectively, are all of order TK, as expected, with BA = BT = BV = 0.75073TK in the Kondo limit.},
doi = {10.1103/PhysRevB.98.075404},
journal = {Physical Review B},
number = 7,
volume = 98,
place = {United States},
year = {2018},
month = {8}
}
Web of Science
Works referenced in this record:
Shot noise near the unitary limit of a Kondo quantum dot
journal, June 2006
 Golub, A.
 Physical Review B, Vol. 73, Issue 23
Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces
journal, May 2009
 Žitko, R.; Peters, R.; Pruschke, Th
 New Journal of Physics, Vol. 11, Issue 5
Equilibrium Fermiliquid coefficients for the fully screened $N$ channel Kondo model
journal, May 2014
 Hanl, M.; Weichselbaum, A.; von Delft, J.
 Physical Review B, Vol. 89, Issue 19
Admittance of the SU(2) and SU(4) Anderson quantum $RC$ circuits
journal, July 2013
 Filippone, Michele; Le Hur, Karyn; Mora, Christophe
 Physical Review B, Vol. 88, Issue 4
Perturbation Expansion for the Anderson Hamiltonian. III
journal, May 1975
 Yosida, K.; Yamada, K.
 Progress of Theoretical Physics, Vol. 53, Issue 5
Green’s Functions from RealTime BoldLine Monte Carlo Calculations: Spectral Properties of the Nonequilibrium Anderson Impurity Model
journal, April 2014
 Cohen, Guy; Gull, Emanuel; Reichman, David R.
 Physical Review Letters, Vol. 112, Issue 14
Perturbation Expansion for the Anderson Hamiltonian. II
journal, April 1975
 Yamada, K.
 Progress of Theoretical Physics, Vol. 53, Issue 4
Critical theory of overscreened Kondo fixed points
journal, August 1991
 Affleck, Ian; Ludwig, Andreas W. W.
 Nuclear Physics B, Vol. 360, Issue 23
Exact lowtemperature results for transport properties of the interacting resonant level model
journal, January 2008
 Boulat, E.; Saleur, H.
 Physical Review B, Vol. 77, Issue 3
Perturbation Analysis on OrbitalDegenerate Anderson Model
journal, January 1976
 Yoshimori, A.
 Progress of Theoretical Physics, Vol. 55, Issue 1
Fermi liquid theory and magnetic impurity systems. I. Quasiparticle Hamiltonians and mean field theory
journal, August 1993
 Hewson, A. C.
 Journal of Physics: Condensed Matter, Vol. 5, Issue 34
Energyresolved inelastic electron scattering off a magnetic impurity
journal, November 2005
 Garst, Markus; Wölfle, Peter; Borda, László
 Physical Review B, Vol. 72, Issue 20
Toulouse limit for the nonequilibrium Kondo impurity: Currents, noise spectra, and magnetic properties
journal, December 1998
 Schiller, Avraham; Hershfield, Selman
 Physical Review B, Vol. 58, Issue 22
Ground State of Asymmetric Anderson Hamiltonian
journal, July 1982
 Kawakami, Norio; Okiji, Ayao
 Journal of the Physical Society of Japan, Vol. 51, Issue 7
The Kondo effect in coupledquantum dots
journal, August 2009
 Chang, A. M.; Chen, J. C.
 Reports on Progress in Physics, Vol. 72, Issue 9
Comparative study of theoretical methods for nonequilibrium quantum transport
journal, April 2010
 Eckel, J.; HeidrichMeisner, F.; Jakobs, S. G.
 New Journal of Physics, Vol. 12, Issue 4
Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
journal, September 2015
 Dorda, Antonius; Ganahl, Martin; Evertz, Hans Gerd
 Physical Review B, Vol. 92, Issue 12
The Kondo Effect in NonEquilibrium Quantum Dots: Perturbative Renormalization Group
journal, January 2005
 Rosch, A.; Paaske, J.; Kroha, J.
 Journal of the Physical Society of Japan, Vol. 74, Issue 1
Nonabelian symmetries in tensor networks: A quantum symmetry space approach
journal, December 2012
 Weichselbaum, Andreas
 Annals of Physics, Vol. 327, Issue 12
Fermi liquid theory of the degenerate anderson model
journal, January 1978
 Mihály, L.; Zawadowski, A.
 Journal de Physique Lettres, Vol. 39, Issue 24
Fermi Liquid Theory for the Nonequilibrium Kondo Effect at Low Bias Voltages
journal, January 2005
 Oguri, Akira
 Journal of the Physical Society of Japan, Vol. 74, Issue 1
Kondo Effect in a Magnetic Field and the Magnetoresistivity of Kondo Alloys
journal, August 2000
 Costi, T. A.
 Physical Review Letters, Vol. 85, Issue 7, p. 15041507
 Article No. 1504
Perturbation Expansion for the Anderson Hamiltonian. IV
journal, August 1975
 Yamada, K.
 Progress of Theoretical Physics, Vol. 54, Issue 2
At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the lowenergy properties of the Anderson model
journal, April 2017
 Filippone, Michele; Moca, Cătălin Paşcu; von Delft, Jan
 Physical Review B, Vol. 95, Issue 16
Magnetic field dependence of the spin ${\scriptstyle \frac{1}{2}}$ and spin1 Kondo effects in a quantum dot
journal, December 2007
 Quay, C. H. L.; Cumings, John; Gamble, S. J.
 Physical Review B, Vol. 76, Issue 24
SteadyState Currents through Nanodevices: A ScatteringStates Numerical RenormalizationGroup Approach to Open Quantum Systems
journal, August 2008
 Anders, Frithjof B.
 Physical Review Letters, Vol. 101, Issue 6
Theory of the atomic limit of the Anderson model. I. Perturbation expansions reexamined
journal, December 1978
 Haldane, F. D. M.
 Journal of Physics C: Solid State Physics, Vol. 11, Issue 24
Spin and charge dynamics in a renormalized perturbation theory
journal, January 2006
 Hewson, A. C.
 Journal of Physics: Condensed Matter, Vol. 18, Issue 5
Kondo temperature dependence of the Kondo splitting in a singleelectron transistor
journal, July 2005
 Amasha, S.; Gelfand, I. J.; Kastner, M. A.
 Physical Review B, Vol. 72, Issue 4
Highorder terms in the renormalized perturbation theory for the Anderson impurity model
journal, September 2015
 Pandis, Vassilis; Hewson, Alex C.
 Physical Review B, Vol. 92, Issue 11
Theory of nonequilibrium transport in the $\text{SU}\left(N\right)$ Kondo regime
journal, October 2009
 Mora, Christophe; Vitushinsky, Pavel; Leyronas, Xavier
 Physical Review B, Vol. 80, Issue 15
Higherorder Fermiliquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport
journal, January 2018
 Oguri, Akira; Hewson, A. C.
 Physical Review B, Vol. 97, Issue 3
Exact results in the theory of magnetic alloys
journal, January 1983
 Tsvelick, A. M.; Wiegmann, P. B.
 Advances in Physics, Vol. 32, Issue 4
Exact solution of the Anderson model. II. Thermodynamic properties at finite temperatures
journal, April 1983
 Tsvelick, A. M.; Wiegmann, P. B.
 Journal of Physics C: Solid State Physics, Vol. 16, Issue 12
Exact solution of the Anderson model: I
journal, April 1983
 Wiegmann, P. B.; Tsvelick, A. M.
 Journal of Physics C: Solid State Physics, Vol. 16, Issue 12
Adaptive broadening to improve spectral resolution in the numerical renormalization group
journal, December 2016
 Lee, SeungSup B.; Weichselbaum, Andreas
 Physical Review B, Vol. 94, Issue 23
OutofEquilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the StrongCoupling Regime
journal, May 2014
 Freton, L.; Boulat, E.
 Physical Review Letters, Vol. 112, Issue 21
Transport properties of fully screened Kondo models
journal, April 2014
 Hörig, Christoph B. M.; Mora, Christophe; Schuricht, Dirk
 Physical Review B, Vol. 89, Issue 16
HigherOrder FermiLiquid Corrections for an Anderson Impurity Away from Half Filling
journal, March 2018
 Oguri, Akira; Hewson, A. C.
 Physical Review Letters, Vol. 120, Issue 12
Kondo physics in tunable semiconductor nanowire quantum dots
journal, December 2006
 Jespersen, Thomas Sand; Aagesen, Martin; Sørensen, Claus
 Physical Review B, Vol. 74, Issue 23
Kondo effect in quantum dots
journal, April 2004
 Pustilnik, Michael; Glazman, Leonid
 Journal of Physics: Condensed Matter, Vol. 16, Issue 16
Fermiliquid theory for the singleimpurity Anderson model
journal, August 2015
 Mora, Christophe; Moca, Cătălin Paşcu; von Delft, Jan
 Physical Review B, Vol. 92, Issue 7
Landauer formula for the current through an interacting electron region
journal, April 1992
 Meir, Yigal; Wingreen, Ned S.
 Physical Review Letters, Vol. 68, Issue 16
Nonequilibrium frequencydependent noise through a quantum dot: A realtime functional renormalization group approach
journal, May 2011
 Moca, C. P.; Simon, P.; Chung, C. H.
 Physical Review B, Vol. 83, Issue 20
Fermiliquid theory for $\text{SU}\left(N\right)$ Kondo model
journal, September 2009
 Mora, Christophe
 Physical Review B, Vol. 80, Issue 12
Measurements of Kondo and Spin Splitting in SingleElectron Transistors
journal, October 2004
 Kogan, A.; Amasha, S.; GoldhaberGordon, D.
 Physical Review Letters, Vol. 93, Issue 16
Renormalization group and Fermi liquid theory
journal, August 1994
 Hewson, A. C.
 Advances in Physics, Vol. 43, Issue 4
New Study of Shot Noise Based on the Nonequilibrium Kubo Formula in Mesoscopic Systems: Application to the Kondo Effect in a Quantum Dot
journal, April 2010
 Fujii, Tatsuya
 Journal of the Physical Society of Japan, Vol. 79, Issue 4
Shot noise in mesoscopic conductors
journal, September 2000
 Blanter, Ya. M.; Büttiker, M.
 Physics Reports, Vol. 336, Issue 12
Kondo crossover in shot noise of a single quantum dot with orbital degeneracy
journal, February 2011
 Sakano, R.; Fujii, T.; Oguri, A.
 Physical Review B, Vol. 83, Issue 7
Renormalized parameters for impurity models
journal, August 2004
 Hewson, A. C.; Oguri, A.; Meyer, D.
 The European Physical Journal B, Vol. 40, Issue 2
Keldysh effective action theory for universal physics in spin $\frac{1}{2}$ Kondo dots
journal, March 2013
 Smirnov, Sergey; Grifoni, Milena
 Physical Review B, Vol. 87, Issue 12
MagneticFieldInduced Crossover to a Nonuniversal Regime in a Kondo Dot
journal, July 2009
 Liu, TaiMin; Hemingway, Bryan; Kogan, Andrei
 Physical Review Letters, Vol. 103, Issue 2
Scaling of conductance through quantum dots with magnetic field
journal, November 2015
 Hamad, I. J.; Gazza, C.; Andrade, J. A.
 Physical Review B, Vol. 92, Issue 19
Anomalous Magnetic Splitting of the Kondo Resonance
journal, August 2000
 Moore, Joel E.; Wen, XiaoGang
 Physical Review Letters, Vol. 85, Issue 8
Variational matrixproductstate approach to quantum impurity models
journal, October 2009
 Weichselbaum, A.; Verstraete, F.; Schollwöck, U.
 Physical Review B, Vol. 80, Issue 16
Perturbational scaling theory of the induced magnetization in the impurity Anderson model
journal, April 2013
 Edwards, K.; Hewson, A. C.; Pandis, V.
 Physical Review B, Vol. 87, Issue 16
Transport properties and Kondo correlations in nanostructures: Timedependent DMRG method applied to quantum dots coupled to Wilson chains
journal, November 2008
 Dias da Silva, Luis G. G. V.; HeidrichMeisner, F.; Feiguin, A. E.
 Physical Review B, Vol. 78, Issue 19
Fractional Shot Noise in the Kondo Regime
journal, August 2006
 Sela, Eran; Oreg, Yuval; von Oppen, Felix
 Physical Review Letters, Vol. 97, Issue 8
Energy resolution and discretization artifacts in the numerical renormalization group
journal, February 2009
 Žitko, Rok; Pruschke, Thomas
 Physical Review B, Vol. 79, Issue 8
Renormalized perturbation calculations for the singleimpurity Anderson model
journal, October 2001
 Hewson, A. C.
 Journal of Physics: Condensed Matter, Vol. 13, Issue 44
Functional renormalization group for nonequilibrium quantum manybody problems
journal, January 2007
 Gezzi, R.; Pruschke, Th.; Meden, V.
 Physical Review B, Vol. 75, Issue 4
The renormalization group: Critical phenomena and the Kondo problem
journal, October 1975
 Wilson, Kenneth G.
 Reviews of Modern Physics, Vol. 47, Issue 4
Fielddependent quasiparticles in a strongly correlated local system. II.
journal, July 2007
 Bauer, J.; Hewson, A. C.
 Physical Review B, Vol. 76, Issue 3
Exact conformalfieldtheory results on the multichannel Kondo effect: Singlefermion Green’s function, selfenergy, and resistivity
journal, September 1993
 Affleck, Ian; Ludwig, Andreas W. W.
 Physical Review B, Vol. 48, Issue 10
Full Counting Statistics for the Kondo Dot in the Unitary Limit
journal, July 2006
 Gogolin, A. O.; Komnik, A.
 Physical Review Letters, Vol. 97, Issue 1
Higherorder Fermiliquid corrections for an Anderson impurity away from half filling : Equilibrium properties
journal, January 2018
 Oguri, Akira; Hewson, A. C.
 Physical Review B, Vol. 97, Issue 4
Functional renormalization group approach to correlated fermion systems
journal, March 2012
 Metzner, Walter; Salmhofer, Manfred; Honerkamp, Carsten
 Reviews of Modern Physics, Vol. 84, Issue 1
Nonequilibrium Kondo model: Crossover from weak to strong coupling
journal, June 2012
 Pletyukhov, Mikhail; Schoeller, Herbert
 Physical Review Letters, Vol. 108, Issue 26
Nonequilibrium differential conductance through a quantum dot in a magnetic field
journal, August 2005
 Hewson, A. C.; Bauer, J.; Oguri, A.
 Journal of Physics: Condensed Matter, Vol. 17, Issue 35
A new renormalization group approach for systems with strong electron correlation
journal, January 2011
 Edwards, K.; Hewson, A. C.
 Journal of Physics: Condensed Matter, Vol. 23, Issue 4
The Strong Coupling FixedPoint Revisited
journal, January 2005
 C. Hewson, A.
 Journal of the Physical Society of Japan, Vol. 74, Issue 1
RealTime Dynamics in QuantumImpurity Systems: A TimeDependent Numerical RenormalizationGroup Approach
journal, October 2005
 Anders, Frithjof B.; Schiller, Avraham
 Physical Review Letters, Vol. 95, Issue 19
Towards an exact solution of the Anderson model
journal, November 1980
 Wiegmann, P. B.
 Physics Letters A, Vol. 80, Issue 23
Kondo Effect in Electromigrated Gold Break Junctions
journal, September 2005
 Houck, A. A.; Labaziewicz, J.; Chan, E. K.
 Nano Letters, Vol. 5, Issue 9
SumRule Conserving Spectral Functions from the Numerical Renormalization Group
journal, August 2007
 Weichselbaum, Andreas; von Delft, Jan
 Physical Review Letters, Vol. 99, Issue 7
Effects of Fermi Liquid Interactions on the Shot Noise of an $\mathrm{SU}(N)$ Kondo Quantum Dot
journal, January 2008
 Vitushinsky, P.; Clerk, A. A.; Le Hur, K.
 Physical Review Letters, Vol. 100, Issue 3
Numerical renormalization group method for quantum impurity systems
journal, April 2008
 Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
 Reviews of Modern Physics, Vol. 80, Issue 2
Universal aspects of nonequilibrium currents in a quantum dot
journal, June 2006
 Doyon, Benjamin; Andrei, Natan
 Physical Review B, Vol. 73, Issue 24
Full counting statistics for SU( $N$ ) impurity Anderson model
journal, June 2011
 Sakano, Rui; Oguri, Akira; Kato, Takeo
 Physical Review B, Vol. 83, Issue 24
Current Noise through a Kondo Quantum Dot in a $\mathrm{SU}(N)$ Fermi Liquid State
journal, January 2008
 Mora, Christophe; Leyronas, Xavier; Regnault, Nicolas
 Physical Review Letters, Vol. 100, Issue 3
Tensor networks and the numerical renormalization group
journal, December 2012
 Weichselbaum, Andreas
 Physical Review B, Vol. 86, Issue 24
Kondo effect for spin 1/2 impurity a minimal effort scaling approach
journal, January 1978
 Nozières, P.
 Journal de Physique, Vol. 39, Issue 10
Nonequilibrium selfenergies, Ng approach, and heat current of a nanodevice for small bias voltage and temperature
journal, March 2014
 Aligia, A. A.
 Physical Review B, Vol. 89, Issue 12
Perturbation of infrared fixed points and duality in quantum impurity problems
journal, May 1999
 Lesage, F.; Saleur, H.
 Nuclear Physics B, Vol. 546, Issue 3
Scaling Theory of the Asymmetric Anderson Model
journal, February 1978
 Haldane, F. D. M.
 Physical Review Letters, Vol. 40, Issue 6
Kondo effect in a singleelectron transistor
journal, January 1998
 GoldhaberGordon, D.; Shtrikman, Hadas; Mahalu, D.
 Nature, Vol. 391, Issue 6663, p. 156159
A ?fermiliquid? description of the Kondo problem at low temperatures
journal, October 1974
 Nozi�res, P.
 Journal of Low Temperature Physics, Vol. 17, Issue 12
Scaling and Decoherence in the Nonequilibrium Kondo Model
journal, July 2005
 Kehrein, Stefan
 Physical Review Letters, Vol. 95, Issue 5
A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Realtime RG in frequency space (RTRGFS)
journal, February 2009
 Schoeller, H.
 The European Physical Journal Special Topics, Vol. 168, Issue 1
Universal OutofEquilibrium Transport in KondoCorrelated Quantum Dots: Renormalized Dual Fermions on the Keldysh Contour
journal, January 2013
 Muñoz, Enrique; Bolech, C. J.; Kirchner, Stefan
 Physical Review Letters, Vol. 110, Issue 1
Renormalized perturbation expansions and Fermi liquid theory
journal, June 1993
 Hewson, A. C.
 Physical Review Letters, Vol. 70, Issue 25
Keldysh technique and nonlinear σmodel: basic principles and applications
journal, May 2009
 Kamenev, Alex; Levchenko, Alex
 Advances in Physics, Vol. 58, Issue 3
Nonequilibrium conductance of a nanodevice for small bias voltage
journal, December 2011
 Aligia, A. A.
 Journal of Physics: Condensed Matter, Vol. 24, Issue 1
StrongCoupling Resistivity in the Kondo Model
journal, May 1999
 Lesage, F.; Saleur, H.
 Physical Review Letters, Vol. 82, Issue 22
Fermiliquid theory for the Anderson model out of equilibrium
journal, September 2001
 Oguri, Akira
 Physical Review B, Vol. 64, Issue 15
OnSite Coulomb Repulsion and Resonant Tunneling
journal, October 1988
 Ng, Tai Kai; Lee, Patrick A.
 Physical Review Letters, Vol. 61, Issue 15
Field dependent quasiparticles in a strongly correlated local system
journal, January 2006
 Hewson, A. C.; Bauer, J.; Koller, W.
 Physical Review B, Vol. 73, Issue 4
Perturbation Expansion for the Anderson Hamiltonian
journal, January 1970
 Yosida, Kei; Yamada, Kosaku
 Progress of Theoretical Physics Supplement, Vol. 46
Magnetic field effects in fewlevel quantum dots: Theory and application to experiment
journal, September 2011
 Wright, Christopher J.; Galpin, Martin R.; Logan, David E.
 Physical Review B, Vol. 84, Issue 11
Nonequilibrium Transport through a Kondo Dot in a Magnetic Field: Perturbation Theory and Poor Man’s Scaling
journal, February 2003
 Rosch, A.; Paaske, J.; Kroha, J.
 Physical Review Letters, Vol. 90, Issue 7