Functional renormalization group for non-equilibrium quantum many-body problems

TL;DR

This paper develops a functional renormalization group method tailored for non-equilibrium quantum many-body systems, enabling analysis of stationary and dynamic states, exemplified by quantum dot transport under bias.

Contribution

It introduces a general non-equilibrium FRG framework using the Keldysh formalism, deriving coupled equations for vertex functions and applying them to quantum dot transport.

Findings

Successfully extended FRG to non-equilibrium scenarios.

Derived coupled differential equations for vertex functions.

Applied method to quantum dot transport with Coulomb interactions.

Abstract

We extend the concept of the functional renormalization for quantum many-body problems to non-equilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations for the $m$-particle vertex functions. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations at finite bias voltage employing two different truncation schemes for the infinite hierarchy of equations arising in the functional renormalization group scheme.