Quantum Monte Carlo for correlated out-of-equilibrium nanoelectronic devices

Rosario E. V. Profumo (1) , Christoph Groth (1) , Laura Messio (2, 3) , Olivier Parcollet (3) , Xavier Waintal (1, 4)

1 SPSMS - UMR 9001 - Service de Physique Statistique, Magnétisme et Supraconductivité
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681
4 GT - Laboratory of Quantum Theory

We 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 U n (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 coefficients of the expansion can easily be obtained for long time, stationary regimes, even at zero temperature. We then 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. Standard extrapolation methods of divergent series can be used to evaluate the series in the strong correlation regime.

Domaines: Physique [physics]

Rosario E. V. Profumo, Christoph Groth, Laura Messio, Olivier Parcollet, Xavier Waintal. Quantum Monte Carlo for correlated out-of-equilibrium nanoelectronic devices. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2015, 91 (24), pp.5154. ⟨10.1103/PhysRevB.91.245154⟩. ⟨cea-01336671⟩