Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model

TL;DR

This paper develops optimized weak-coupling quantum Monte Carlo methods on the Keldysh contour for nonequilibrium quantum transport, enabling accurate simulations of the Anderson model's current-voltage characteristics over wider parameters.

Contribution

It introduces and compares two system preparation methods for nonequilibrium Monte Carlo simulations and enhances measurement efficiency, extending the range of accurate quantum dot transport modeling.

Findings

Monte Carlo accurately simulates transport for large interactions and long times.

Perturbation theory fails at U/Gamma>4.

No evidence of Kondo resonance splitting under voltage.

Abstract

We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the real-time calculation: the "interaction quench" and the "voltage quench", which are found to be suitable for large and small voltage biasses, respectively. We also discuss technical optimizations which increase the efficiency of the real-time measurements. The methods allow the accurate simulation of transport through quantum dots over wider interaction ranges and longer times than have heretofore been possible. The current-voltage characteristics of the particle-hole symmetric Anderson impurity model is presented for interactions U up to 10 times the intrinsic level width Gamma. We compare the Monte Carlo results to fourth order perturbation theory, finding that perturbation theory begins to fail at U/Gamma>4. Within the parameter range studied we find no evidence for a splitting of the Kondo resonance due to the applied voltage. The interplay of voltage and temperature and the Coulomb blockade conductance regime are studied.