Effective Equilibrium Theory of Nonequilibrium Quantum Transport
arXiv:1101.1526 · doi:10.1016/j.aop.2011.07.001
Abstract
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate the Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field.
53 pages, 6 figures, Final Version to be published in Annals of Physics
References in corpus (18)
- Continuous-time Monte Carlo methods for quantum impurity models
- Observation of the two-channel Kondo effect
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
- Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
- Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
- A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
- Transient dynamics of the Anderson impurity model out of equilibrium
- Noisy Kondo impurities
- Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
- New method for studying steady states in quantum impurity problems: The interacting resonant level model
- Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces
- Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state
- Shot Noise in SU(N) Quantum Dot Kondo Effects
- Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data
- Phonon-assisted tunneling and two-channel Kondo physics in molecular junctions
- Full counting statistics of spin transfer through ultrasmall quantum dots
- Failure of mean-field approach in out-of-equilibrium Anderson model
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- How to construct the proper gauge-invariant density matrix in steady-state nonequilibrium: Applications to spin-transfer and spin-orbit torques
- Theory of Entropy Production in Quantum Many-Body Systems
- Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach
- Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator
- Strongly-Correlated Thermoelectric Transport beyond Linear Response
- Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
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- Nonequilibrium distribution functions for quantum transport: universality and approximation for the steady state regime
- Impurity model for non-equilibrium steady states
- Non-equilibrium quantum transport through a dissipative resonant level
- Non-equilibrium charge susceptibility and dynamical conductance: Identification of scattering processes in quantum transport
- Exact interacting Green's function for the Anderson impurity at high bias voltages
- Nonlinear Fermi-liquid transport through a quantum dot in asymmetric tunnel junctions
- Quantum Recurrences in a One-Dimensional Gas of Impenetrable Bosons
- Reconciling Kubo and Keldysh Approaches to Fermi-Sea-Dependent Nonequilibrium Observables: Application to Spin Hall Current and Spin-Orbit Torque in Spintronics