The excitation operator approach to non-Markovian dynamics of quantum impurity models in the Kondo regime

TL;DR

This paper introduces a numerical method based on excitation operators to study the real-time non-Markovian dynamics of quantum impurity models in the Kondo regime, capturing environmental back-actions and electron interactions.

Contribution

The paper develops a novel operator-based numerical approach that simplifies the analysis of non-Markovian quantum impurity dynamics in the Kondo regime.

Findings

Coexistence of Kondo correlation and non-Markovian reservoir causes coherence ringings.

Coherence ringings are suppressed by system driving away from particle-hole symmetry.

Transition to a Markovian reservoir diminishes the coherence effects.

Abstract

We present a numerical method for studying the real time dynamics of a small interacting quantum system coupled to an infinite fermionic reservoir. By building an orthonormal basis in the operator space, we turn the Heisenberg equation of motion into a system of linear differential equations, which is then solved iteratively by constructing excitation operators. The application of our method depends on a layer structure in the operator space, which help us to turn an infinite linear system into a series of small systems. We apply the method to investigate the decoherence dynamics of quantum impurity models in the Kondo regime with a non-Markovian reservoir. Taking full account of environmental back-actions and electron-electron interactions, we find that the coexistence of the Kondo correlation and a non-Markovian reservoir induces coherence ringings, which will be suppressed by either driving the system away from the particle-hole symmetric point or changing the reservoir into a Markovian one.