Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation

TL;DR

This paper investigates the relaxation dynamics of a strongly-interacting two-site Fermi-Hubbard model coupled to fermionic baths, deriving Lindblad operators microscopically and comparing different approximation methods across temperature regimes.

Contribution

It provides a microscopic derivation of non-local Lindblad operators for a Hubbard dimer coupled to baths and introduces an improved secular approximation called the coherent approximation.

Findings

Non-local Lindblad operators are necessary despite local bath coupling.

The coherent approximation outperforms the secular approximation in all tested regimes.

Comparison of methods reveals differences in early and late time relaxation dynamics.

Abstract

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by coupling each site to a local fermionic bath. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the time evolution of the reduced density matrix. In spite of a local coupling to the baths, the found Lindblad operators are non-local in space. We compare with the local approximation, where those non-local effects are neglected. Furthermore, we propose an improvement on the commonly-used secular approximation (rotating-wave approximation), referred to as coherent approximation, which turns out superior in all studied parameter regimes (and equivalent otherwise). We look at the relaxation dynamics for several important observables and compare the methods for early and late times in various temperature regimes.