From thermal equilibrium to nonequilibrium quench dynamics: A conserving approximation for the interacting resonant level

TL;DR

This paper introduces a conserving approximation method for the interacting resonant-level model, accurately describing equilibrium, nonequilibrium steady states, and quench dynamics, with analytical and numerical validation of key physical phenomena.

Contribution

It develops a low-order conserving approximation that captures equilibrium and nonequilibrium dynamics, including power-law behaviors and quench responses, validated against established methods.

Findings

Good agreement with other methods in equilibrium for small interactions

Analytical derivation of power-law exponents for level width and current suppression

Observation of negative differential conductance at high voltages

Abstract

We develop a low-order conserving approximation for the interacting resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii) nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal equilibrium is first used to carefully gauge the quality of the approximation by comparing the results with other well-studied methods, and finding good agreement for small values of the interaction. We analytically show that the power-law exponent of the renormalized level width usually derived using renormalization group approaches can also be correctly obtained in our approach in the weak interaction limit. A closed expression for the nonequilibrium steady-state current is derived and analytically and numerically evaluated. We find a negative differential conductance at large voltages, and the exponent of the power-law suppression of the steady-state current is calculated analytically at zero-temperature. The response of the system to quenches is investigated for a single-lead as well as for two-lead setup at finite voltage bias at particle-hole symmetry using a self-consistent two-times Keldysh Green function approach, and results are presented for the time-dependent current for different bias and contact interaction strength.