Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties

TL;DR

This paper establishes a formal equivalence between imaginary-time and real-time quantum many-body theories for nonequilibrium systems, specifically quantum dots, and demonstrates how to calculate static properties using the Matsubara voltage approach.

Contribution

It introduces a formal connection between Keldysh real-time and imaginary-time theories and applies the Matsubara voltage method to compute static properties in non-equilibrium quantum dots.

Findings

Established conditions for correct analytic continuation

Applied the method to quantum dot steady-state calculations

Identified limitations of the Matsubara voltage approach

Abstract

We discuss the formal relationship between the real-time Keldysh and imaginary-time theory for nonequilibrium in quantum dot systems. The latter can be reformulated using the recently proposed Matsubara voltage approach. We establish general conditions for correct analytic continuation procedure on physical observables, and apply the technique to the calculation of static quantities in steady-state non-equilibrium for a quantum dot subject to a finite bias voltage and external magnetic field. Limitations of the Matsubara voltage approach are also pointed out.