Perturbative expansion of the magnetization in the out-of-equilibrium Kondo model

Parcollet, Olivier; Hooley, C.

doi:10.1103/physrevb.66.085315

Cited by 58 publications

(88 citation statements)

References 25 publications

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“…It can be applied to any single-impurity model with linear spectrum and with left-/right-moving separation of the leads' quasi-particles (where unfolding can be done): Kondo and Anderson models, and impurity models where leads are Luttinger liquids (bosonic collective modes separate). In the non-equilibrium Kondo model with an impurity magnetic field, it may simplify the treatment of the pathologic perturbative expansion [4]. Although our method may be restricted to integrable dynamics (this is to be clarified), it does not rely on integrability of the steady state; the non-equilibrium steady states in the Kondo and Anderson models may not be integrable.…”

Section: The Hamiltonian Ismentioning

confidence: 99%

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New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

Doyon

2007

Phys. Rev. Lett.

101

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We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density matrix along with dynamical "impurity conditions". This gives the full perturbative expansion without Feynman diagrams (matrix products instead are used), and "re-sums" into an equilibrium average that may lend itself to numerical procedures. We calculate the universal current in the interacting resonant level model (IRLM) at finite bias V to first order in Coulomb repulsion U for all V and temperatures. We find that the bias, like the temperature, cuts off low-energy processes. In the IRLM, this implies a power-law decay of the current at large V (also recently observed by Boulat and Saleur at some finite value of U ).PACS numbers: 73.63. Kv, 72.15.Qm, 72.10.Fk Impurity models describe mesoscopic quantum objects in contact with large conducting leads. Quantum dots are much-studied examples, and experiments in a bias voltage [1] lead to accurate descriptions of their nonequilibrium steady-state properties. In impurity models, such states are of high interest as they pose the theoretical challenge of capturing the effect of non-equilibrium in a truly quantum system, yet they constitute the simplest non-equilibrium situation, where properties are time independent. At low energies, interactions between the leads' Landau quasi-particles and the impurity occur in the s-wave channel, and the spectrum may be linearised around the two Fermi points. Then, the universal behaviour is described by free massless fermions on the half line (bulk conformal field theory) with a non-conformal boundary interaction at the end-point. Many methods are known for studying equilibrium behaviors in such models, but understanding and accessing properties of non-equilibrium steady states is still a much harder task. Wilson's picture does not apply, and, for instance, the effect of a bias on low-energy processes (which determines the large-bias current) is still under study [2,3].Two calculational schemes exist:the real-time Schwinger-Keldysh formulation and the scattering-state Lippman-Schwinger formulation. The former relies on the infinite extent of the half line in order to absorb the energy released by relaxation from an appropriate "uninteracting" density matrix to the steady state. It requires relaxation mechanisms (see, e.g. [3]), whose absence may lead to pathologies in perturbative expansions [4]. The latter describes directly the expected end result just from "how the state looks" asymptotically far from the impurity. Hershfield's Y operator [5] (see also the studies [3,6,7]) gives a "steady-state density matrix" that encodes these scattering states. This is interesting, since a non-equilibrium steady state is not described by the usual density matrix, but it is still hard to apply to interacting systems. Exact results for integable models occur when the exact quasi-particles do not mix the bias...

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Section: The Hamiltonian Ismentioning

confidence: 99%

“…It requires relaxation mechanisms (see, e.g. [3]), whose absence may lead to pathologies in perturbative expansions [4]. The latter describes directly the expected end result just from "how the state looks" asymptotically far from the impurity.…”

mentioning

confidence: 99%

New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

Doyon

2007

Phys. Rev. Lett.

101

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“…Theoretically, the Kondo effect out of equilibrium has been studied by a number of methods ranging from perturbation theory, 9,10,12,27,28,[39][40][41][42][43][44][45][46] equations of motions and self-consistent diagrammatic methods 30,[47][48][49][50][51][52][53][54][55] (using the so-called non-crossing approximation), slave-boson mean-field theories, 57-59 exact solutions for some variants of the Kondo model with appropriately chosen coupling constants, 56 the construction of approximate scattering states starting from Bethe ansatz solutions, 60 to perturbative renormalization group 28,43,61 (reviewed below). It is, however, important to note, that many of the methods which have been so successful in equilibrium cannot or have not yet been generalized even to the simplest steady-state non-equilibrium situation.…”

Section: -35mentioning

confidence: 99%

The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group

et al. 2005

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While the properties of the Kondo model in equilibrium are very well understood, much less is known for Kondo systems out of equilibrium. We study the properties of a quantum dot in the Kondo regime, when a large bias voltage V and/or a large magnetic field B is applied. Using the perturbative renormalization group generalized to stationary nonequilibrium situations, we calculate renormalized couplings, keeping their important energy dependence. We show that in a magnetic field the spin occupation of the quantum dot is non-thermal, being controlled by V and B in a complex way to be calculated by solving a quantum Boltzmann equation. We find that the well-known suppression of the Kondo effect at finite V ≫ TK (Kondo temperature) is caused by inelastic dephasing processes induced by the current through the dot. We calculate the corresponding decoherence rate, which serves to cut off the RG flow usually well inside the perturbative regime (with possible exceptions). As a consequence, the differential conductance, the local magnetization, the spin relaxation rates and the local spectral function may be calculated for large V, B ≫ TK in a controlled way.

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“…To average the product of dot spin operators we express them in terms of mixed Dirac (f, f † ) and Majorana (η x , η y , η z ) fermions [17]:…”

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confidence: 99%

Kondo Correlations and Majorana Bound States in a Metal to Quantum-Dot to Topological-Superconductor Junction

2011

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Electron transport through [normal metal]-[quantum dot]-[topological superconductor] junction is studied and reveals interlacing physics of Kondo correlations with two Majorana fermions bound state residing on the opposite edges of the topological superconductor. When the strength of the Majorana fermion coupling exceeds the temperature T , this combination of Kono-Majorana fermion physics can be observed: The usual peak of the temperature dependent zero biased conductance σ(V = 0, T ) splits and the conductance has a dip at T = 0. The height of the conductance side-peaks decreases with magnetic field.

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Perturbative expansion of the magnetization in the out-of-equilibrium Kondo model

Cited by 58 publications

References 25 publications

New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

New Method for Studying Steady States in Quantum Impurity Problems: The Interacting Resonant Level Model

The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group

Kondo Correlations and Majorana Bound States in a Metal to Quantum-Dot to Topological-Superconductor Junction

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