New method for studying steady states in quantum impurity problems: The interacting resonant level model

TL;DR

This paper introduces a novel perturbative approach for analyzing steady states in quantum impurity systems, enabling calculations of current and other properties without Feynman diagrams, and applies it to the interacting resonant level model.

Contribution

The paper presents a new perturbative method based on impurity conditions and density matrices that simplifies steady-state calculations in quantum impurity problems.

Findings

Calculated the universal current at finite bias to first order in Coulomb interaction.

Discovered bias and temperature cut off low-energy processes, leading to power-law decay of current.

Validated the method by reproducing known behaviors in the IRLM.

Abstract

We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density matrix along with dynamical "impurity conditions". This gives the full perturbative expansion without Feynman diagrams (matrix products instead are used), and "re-sums" into an equilibrium average that may lend itself to numerical procedures. We calculate the universal current in the interacting resonant level model (IRLM) at finite bias V to first order in Coulomb repulsion U for all V and temperatures. We find that the bias, like the temperature, cuts off low-energy processes. In the IRLM, this implies a power-law decay of the current at large V (also recently observed by Boulat and Saleur at some finite value of U).