Some exact results for the anderson model of an impurity

U. Brandt, Andreas Giesekus

G. Shankar Ganesh, Joseph Maciejko

Omamoke O. E. Enaroseha, John Andikara

The ground-state energy, wave-function, hybridization gap and magnetic phasediagram of the Single Site Impurity Anderson Model (SIAM) and the Periodic AndersonModel (PAM) were calculated using Exact-Diagonalization (ED) technique. The EDtechnique was applied to the SIAM and PAM in one dimension before speculating on Ce 4fbeing a test bed of the results, since it has 4f localized electrons in the Heavy fermioncompound CeCu2Si2. Each of the results obtained describe the evolution of the electronicsystem in terms of a simple set of parameters.The parameter regimes studied suggest asmooth phase transition from an antiferromagnetic (AFM) phase to a ferromagnetic (FM)phase at quarter fillings in one dimension when t increases and a magnetic instability wasobserved as U → ∞. The role of hybridization between the conduction electrons and thelocalized f orbital in the Anderson impurity in a semiconductor was also investigated as Vincreases in the SIAM and the PAM.

Lentara Pundi Syaina, Muhammad Aziz Majidi

Single impurity Anderson model describes a system consisting of non-interacting conduction electrons coupled with a localized orbital having strongly interacting electrons at a particular site. This model has been proven successful to explain the phenomenon of metal-insulator transition through Anderson localization. Despite the well-understood behaviors of the model, little has been explored theoretically on how the model properties gradually evolve as functions of hybridization parameter, interaction energy, impurity concentration, and temperature. Here, we propose to do a theoretical study on those aspects of a single impurity Anderson model using the distributional exact diagonalization method. We solve the model Hamiltonian by randomly generating sampling distribution of some conducting electron energy levels with various number of occupying electrons. The resulting eigenvalues and eigenstates are then used to define the local single-particle Green function for each sampled electron energy distribution using Lehmann representation. Later, we extract the corresponding self-energy of each distribution, then average over all the distributions and construct the local Green function of the system to calculate the density of states. We repeat this procedure for various values of those controllable parameters, and discuss our results in connection with the criteria of the occurrence of metal-insulator transition in this system.

U. Brandt, Andreas Giesekus

Bijay Kumar Agarwalla, Dvira Segal

We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green's function formalism, we reach an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady-state current-occupation relation can be used to assess the consistency of simulation techniques and identify spurious transport phenomena. We test this relation in two different model variants: First, we study the Anderson-Holstein model in the strong electron-vibration coupling limit using the polaronic quantum master equation method. We find that the current-occupation relation is violated numerically in standard calculations, with simulations bringing up incorrect transport effects. Using a numerical procedure, we resolve the problem efficiently. Second, we simulate the Anderson model with electron-electron interaction on the dot using a deterministic numerically exact time-evolution scheme. Here, we observe that the current-occupation relation is satisfied in the steady-state limit-even before results converge to the exact limit.