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

TL;DR

This paper introduces a quantum Monte-Carlo algorithm for out-of-equilibrium nanoelectronics, enabling systematic computation of physical observables in interacting systems using diagrammatic expansions, with applications to the Anderson model.

Contribution

The paper presents a general-purpose Monte-Carlo method for out-of-equilibrium systems that sums over Keldysh indices to ensure unitarity and can reach long-time stationary regimes.

Findings

Successfully applied to the Anderson model.

Recovered known results like spin susceptibility and Kondo ridge.

Monte-Carlo free of the sign problem at zero temperature.

Abstract

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 method can easily reach 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.