Interaction-Mediated Non-Reciprocal Dynamics in Open Quantum Systems: From an Exactly Solvable Model to Generic Behavior

TL;DR

This paper demonstrates how density interactions in open quantum systems can transfer non-reciprocal behavior across different degrees of freedom, using an exactly solvable model to reveal new dynamical phenomena.

Contribution

It introduces the Hatsugai-Kohmoto model as a minimal exactly solvable platform for studying interaction-mediated non-reciprocal dynamics in open quantum many-body systems.

Findings

Interactions induce directional drift in spin sectors not directly coupled to the reservoir.

Exact solvability of the Lindbladian dynamics in the model.

Non-reciprocal behavior is transferred between degrees of freedom via interactions.

Abstract

Reservoir engineering has emerged as a powerful paradigm to realize non-reciprocal dynamics in open quantum many-body systems. Here, we show that density-density interactions can transfer bath-induced non-reciprocity between different degrees of freedom. Specifically, we investigate a one-dimensional lattice of spin-$\frac{1}{2}$ fermions with all-to-all Hatsugai-Kohmoto interactions in the presence of an engineered reservoir. We establish the exact solvability of the Lindbladian dynamics and show that the interplay between non-reciprocity and interactions qualitatively reshapes the dynamics of excitations. Remarkably, interactions induce directional drift even in spin sectors that are not directly coupled to the reservoir. By analyzing a driven-dissipative Fermi-Hubbard chain, we show that the same mechanism persists for local interactions. The Hatsugai-Kohmoto model thus emerges as a minimal, exactly solvable platform for interaction-mediated non-reciprocal many-body dynamics.