We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single-impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows one to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions, up to the contacts-dot coupling energy. Besides its simplicity, an additional advantage of the theory is that it correctly describes the unitary limit, giving the correct result for the conductance maximum. Thus our theory establishes an alternative simple method relevant for investigation of weakly interacting nonequilibrium nanodevices.
We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single-impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows one to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions, up to the contacts-dot coupling energy. Besides its simplicity, an additional advantage of the theory is that it correctly describes the unitary limit, giving the correct result for the conductance maximum. Thus our theory establishes an alternative simple method relevant for investigation of weakly interacting nonequilibrium nanodevices.
Kondo physics in nonequilibrium interacting nanoscale devices is an attractive fundamental many-particle phenomenon with a rich potential for applications. Due to enormous complexity its clear and flexible theory is still highly desirable. We develop a physically transparent analytical theory capable of correctly describing the Kondo effect in strongly interacting systems at temperatures close to and above the Kondo temperature. We derive a nonequilibrium Keldysh field theory valid for a system with any finite electron-electron interaction which is much stronger than the coupling of the system to contacts. Finite electron-electron interactions are treated involving as many slave-boson degrees of freedom as one needs for a concrete many-body system. In a small vicinity of the zero slave-bosonic field configuration weak slave-bosonic oscillations, induced by the dot-contacts tunneling, are described by an effective Keldysh action quadratic in the slave-bosonic fields. For clarity the theory is presented for the single impurity Anderson model but the construction of the Keldysh field integral is universal and applicable to systems with more complex many-body spectra.
We present a theory for the Kondo spin-21 effect in strongly correlated quantum dots. The theory is applicable at any temperature and voltage. It is based on a quadratic Keldysh effective action parametrized by a universal function. We provide a general analytical form for the tunneling density of states through this universal function for which we propose a simple microscopic model. We apply our theory to the highly asymmetric Anderson model with $U=\ensuremath{\infty}$ and describe its strong-coupling limit, weak-coupling limit, and crossover region within a single analytical expression. We compare our results with a numerical renormalization group in equilibrium and with a real-time renormalization group out of equilibrium and show that the universal shapes of the linear and differential conductance obtained in our theory and in these theories are very close to each other in a wide range of temperatures and voltages. In particular, as in the real-time renormalization group, we predict that at the Kondo voltage the differential conductance is equal to 2/3 of its maximum.
We present a nonequilibrium nonperturbative field theory for the Kondo effect in strongly interacting quantum dots at finite temperatures. Unifying the slave-boson representation with the Keldysh field integral, an effective Keldysh action is derived and explored in the vicinity of the zero slave-bosonic field configuration. The theory properly reflects the essential features of the Kondo physics and at the same time significantly simplifies a field-theoretic treatment of the phenomenon, avoiding complicated saddle-point analysis or 1/N expansions, used so far. Importantly, our theory admits a closed analytical solution which explains the mechanism of the Kondo effect in terms of an interplay between the real and the imaginary parts of the slave-bosonic self-energy. It thus provides a convenient nonperturbative building block, playing the role of a ``free propagator,'' for more advanced theories. We finally demonstrate that already this simplest possible field theory is able to correctly reproduce experimental data on the Kondo peak observed in the differential conductance, correctly predicts the Kondo temperature, and, within its applicability range, has the same universal temperature dependence of the conductance as the one obtained in numerical renormalization group calculations.
In this thesis, we use a functional quantum field theoretical approach to investigate the non-equilibrium time evolution of an Anderson quantum dot with the main focus on the Kondo regime. We employ a real-time Keldysh path integral formulation to find an effective action. From the two-particle irreducible effective action, we derive, from the variational principle, the exact real-time Kadanoff–Baym equations of motion for the full propagator. We study these dynamic equations for the single impurity Anderson model, which decribes a quantum dot coupled to two finite-temperature leads. We take the tunnelling to the leads into account exactly. In order to solve the Kadanoff–Baym equations numerically we have to approximate them. For this purpose, we make a non-perturbative approximation by summing an infinite number of Feynman diagrams in the direct (s)-, particle-particle (t)-, particle-hole (u)-, and stu-channels. The aim of our investigation is to analyse the non-equilibrium realtime evolution of the quantum dot after a hybridisation and interaction quench into its stationary state. The main focus is on the narrowing of the Kondo resonance and the formation of the Hubbard side bands. Following on from this, the main achievement is the transient, as well as the stationary electrical current, through the quantum dot and the investigation of the dependence on temperature and magnetic field. We compare our results with other methods, such as functional renormalisation group and iterative sum of path integrals, and find a very good agreement in most situations.
In this report, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage V. Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance dI/dV exactly up to terms of order (eV)2 for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution feff(ω), which at eV=0 coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by feff(ω). The residual interaction between the quasiparticles U, which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of U. We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.
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.