Continuous-Time Quantum Monte Carlo and Maximum Entropy Approach to an Imaginary-Time Formulation of Strongly Correlated Steady-State Transport

TL;DR

This paper combines continuous-time quantum Monte Carlo and maximum entropy methods to analyze imaginary-time formulations of steady-state quantum transport, providing a potential pathway to accurately compute spectral functions in strongly correlated systems.

Contribution

It introduces a novel approach integrating quantum Monte Carlo and maximum entropy techniques for imaginary-time steady-state transport analysis.

Findings

Method yields results consistent with other approaches.

Spectral functions can be obtained from complexified voltage data.

Challenges remain in extracting reliable spectral functions at large voltages.

Abstract

Recently Han and Heary proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the non-equilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.