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Mardi 22 septembre 2015-14:00

A numerical approach to many-body diagrammatic theory

Xavier Waintal (CEA Grenoble)

par Gabriel LeMarié - 22 septembre 2015

I will present a simple, general purpose, quantum Monte-Carlo algorithm for out-of-equilibrium interacting nanoelectronics systems. It allows one to systematically compute the expansion of any physical observable (such as current or density) in powers of the electron-electron interaction coupling constant U. It is based on the out-of-equilibrium Keldysh Green’s function formalism in real-time and corresponds to evaluating all the Feynman diagrams to a given order Un (up to n=15 in the present work). A key idea is to explicitly sum over the Keldysh indices in order to enforce the unitarity of the time evolution. The method can easily reach long time, stationary regimes, even at zero temperature.

In a second part I will illustrate our approach with an application to the Anderson model, an archetype interacting mesoscopic system. We recover various results of the literature such as the spin susceptibility or the "Kondo ridge" in the current-voltage characteristics. In this case, we found the Monte-Carlo free of the sign problem even at zero temperature, in the stationary regime and in absence of particle-hole symmetry. The main limitation of the method is the lack of convergence of the expansion in U for large U, i.e. a mathematical property of the model rather than a limitation of the Monte-Carlo algorithm. I will discuss how one can use the analytical structure of the expansion in the complex plane to evaluate the series in the strong correlation regime.

Post-scriptum :

contact : N. Laflorencie