Interaction-Enabled Hartree Fixed Points in Fermionic Resetting Dynamics

TL;DR

This paper extends resetting dynamics in fermionic systems to include weak interactions using a Hartree mean-field approach, revealing new steady states and providing a framework for studying nonequilibrium behavior in interacting open quantum systems.

Contribution

It introduces a controlled mean-field extension of resetting dynamics to weakly interacting fermions, maintaining analytical tractability and enabling the study of interaction-enabled steady states.

Findings

Interaction-enabled steady states not present in quadratic models

Development of a CP-safe Gaussian Lindblad embedding

Numerical validation in ring and two-site models

Abstract

In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are reinitialized between interactions. This provides a versatile route to engineer nonequilibrium steady states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in quadratic fermionic models. The baseline noninteracting resetting scheme yields an affine evolution for the subsystem single-particle density matrix (SPDM), with a clear operational interpretation: a finite environment block E mediates the interaction between the subsystem S and an ideal external thermal reservoir. In this work, we develop a controlled extension of such a framework to weakly interacting systems. We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior. We further construct a completely positive (CP-safe) Gaussian Lindblad embedding that reproduces the resetting dynamics in the noninteracting limit and yields a continuous-time representation of environmental thermalization when interactions are present. Our analytical results are complemented by numerical studies of a ring segmentation geometry and a minimal two-site model, revealing interaction-enabled steady states that cannot be obtained in any purely quadratic setting. Together, these results establish a general and physically consistent route for incorporating weak interactions ino resetting-based approaches to open quantum system.