Imaginary-time quantum many-body theory out of equilibrium II: Analytic continuation of dynamic observables and transport properties

TL;DR

This paper develops a mathematical framework and a maximum-entropy algorithm for analytically continuing imaginary-time quantum Monte Carlo data to real frequencies and voltages, enabling the study of non-equilibrium transport in quantum dots.

Contribution

It introduces a function-theoretical approach and a maximum-entropy method for analytic continuation of dynamical observables in non-equilibrium quantum systems.

Findings

Successfully computed spectral functions in stationary non-equilibrium.

Analyzed current-voltage characteristics for various charging energies.

Demonstrated the feasibility of the analytic continuation method.

Abstract

Within the imaginary-time theory for nonequilibrium in quantum dot systems the calculation of dynamical quantities like Green's functions is possible via a suitable quantum Monte-Carlo algorithm. The challenging task is to analytically continue the imaginary-time data for both complex voltage and complex frequency onto the real variables. To this end a function-theoretical description of dynamical observables is introduced and discussed within the framework of the mathematical theory of several complex variables. We construct a feasible maximum-entropy algorithm for the analytical continuation by imposing a continuity assumption on the analytic structure and provide results for spectral functions in stationary non-equilibrium and current-voltage characteristics for different values of the dot charging energy.