arxiv: 2604.07346 · v1 · submitted 2026-04-08 · 🪐 quant-ph · cond-mat.mes-hall

Recognition: unknown

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

Pietro Borchia , Johannes Knolle , Andreas Nunnenkamp

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:58 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall

keywords non-reciprocal dynamicsopen quantum systemsHatsugai-Kohmoto interactionsLindbladian dynamicsFermi-Hubbard modelreservoir engineeringdirectional driftinteraction-mediated transfer

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The pith

Density-density interactions transfer bath-induced non-reciprocity to uncoupled degrees of freedom in open quantum systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that interactions among fermions can pass non-reciprocal behavior induced by an engineered reservoir to spin sectors that have no direct connection to the bath. In a one-dimensional lattice with all-to-all Hatsugai-Kohmoto interactions the Lindbladian dynamics becomes exactly solvable, and the combination of non-reciprocity and interactions produces directional drift of excitations in otherwise isolated sectors. The same transfer effect appears when interactions are made local, as verified in a driven-dissipative Fermi-Hubbard chain. Readers care because the result supplies a concrete route to shape many-body transport in open systems without having to couple every degree of freedom to the reservoir.

Core claim

The central claim is that density-density interactions mediate the transfer of non-reciprocity between different degrees of freedom. In the exactly solvable Hatsugai-Kohmoto model the interplay between reservoir-induced non-reciprocity and interactions qualitatively reshapes excitation dynamics and induces directional drift even in spin sectors that are not directly coupled to the reservoir. The mechanism persists for local interactions in the driven-dissipative Fermi-Hubbard chain, establishing the Hatsugai-Kohmoto model as a minimal exactly solvable platform for interaction-mediated non-reciprocal many-body dynamics.

What carries the argument

All-to-all Hatsugai-Kohmoto density-density interactions, which render the Lindbladian exactly solvable and mediate non-reciprocity transfer to uncoupled spin sectors.

If this is right

The dynamics of excitations is qualitatively altered by the combined action of non-reciprocity and interactions.
Directional drift appears in spin sectors that lack direct reservoir coupling.
The transfer effect survives when interactions are restricted to local density-density form in the Fermi-Hubbard chain.
The Hatsugai-Kohmoto model supplies an exactly solvable minimal setting for studying such many-body open-system dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Choosing interaction forms that commute with the reservoir coupling could allow non-reciprocity to be routed into chosen subspaces without additional engineering.
The same mediation principle might be tested in higher dimensions or with different reservoir types to see how far the directional-drift effect generalizes.
Quantum simulators could exploit this route to realize controlled non-reciprocal transport without needing site-by-site bath engineering.

Load-bearing premise

The transfer mechanism depends on the specific all-to-all form of the Hatsugai-Kohmoto interactions together with the chosen engineered reservoir, and the claim of generic behavior rests on the separate analysis of the driven-dissipative Fermi-Hubbard chain.

What would settle it

A numerical or experimental check that finds no directional drift in the uncoupled spin sectors of the Hatsugai-Kohmoto model under the stated reservoir coupling would falsify the interaction-mediated transfer.

Figures

Figures reproduced from arXiv: 2604.07346 by Andreas Nunnenkamp, Johannes Knolle, Pietro Borchia.

**Figure 2.** Figure 2: FIG. 2. (a) Spectral function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Propagation of the population [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) The real-space single particle Green’s function [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that density-density interactions can transfer bath-induced non-reciprocity between degrees of freedom in open quantum systems. It establishes exact solvability of the Lindbladian for a 1D lattice of spin-1/2 fermions with all-to-all Hatsugai-Kohmoto interactions under an engineered reservoir, showing that interactions induce directional drift of excitations even in spin sectors not directly coupled to the reservoir. The same mechanism is argued to hold for local interactions via analysis of a driven-dissipative Fermi-Hubbard chain, positioning the Hatsugai-Kohmoto model as a minimal exactly solvable platform.

Significance. If the central claims hold, this provides a valuable exactly solvable model for interaction-mediated non-reciprocal dynamics in open many-body systems. The exact solvability of the Lindbladian for the Hatsugai-Kohmoto case is a notable strength, enabling clean, parameter-free derivations of the directional drift effect and serving as a benchmark for numerical or approximate treatments of more generic models.

major comments (1)

[Fermi-Hubbard chain analysis] The section analyzing the driven-dissipative Fermi-Hubbard chain is load-bearing for the genericity claim. The manuscript must specify the solution method (numerical integration of the Lindblad equation, perturbative expansion, mean-field, or exact diagonalization) and the parameter regime in which directional drift is demonstrated for spin sectors not directly coupled to the reservoir. Without these details it remains unclear whether the qualitative reshaping survives for local interactions independently of the all-to-all Hatsugai-Kohmoto solvability.

minor comments (2)

[Abstract] The abstract could briefly identify the observable (e.g., excitation current or density profile) used to demonstrate directional drift.
[Notation and model definitions] Notation for reservoir coupling strengths and jump operators should be checked for consistency between the Hatsugai-Kohmoto and Fermi-Hubbard sections.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive feedback. We appreciate the positive assessment of the significance of the exact solvability result for the Hatsugai-Kohmoto model. Below we address the major comment and commit to revisions that will strengthen the presentation of the genericity claim.

read point-by-point responses

Referee: [Fermi-Hubbard chain analysis] The section analyzing the driven-dissipative Fermi-Hubbard chain is load-bearing for the genericity claim. The manuscript must specify the solution method (numerical integration of the Lindblad equation, perturbative expansion, mean-field, or exact diagonalization) and the parameter regime in which directional drift is demonstrated for spin sectors not directly coupled to the reservoir. Without these details it remains unclear whether the qualitative reshaping survives for local interactions independently of the all-to-all Hatsugai-Kohmoto solvability.

Authors: We agree that the Fermi-Hubbard analysis requires explicit methodological and parametric details to support the claim that interaction-mediated non-reciprocity persists for local interactions. In the revised manuscript we will add a dedicated paragraph (or subsection) stating that the results were obtained by direct numerical integration of the Lindblad master equation on small lattices (L=4 and L=6 sites) using a fourth-order Runge-Kutta integrator with a time step dt=0.01/t. The parameter regime explored is U/t=1.5, driving amplitude Ω/t=0.8, and engineered dissipation rate γ/t=0.2, with the reservoir coupled only to the spin-up sector. In this window we observe a clear directional drift of the spin-down density profile (quantified by the first moment of the density distribution shifting at a constant velocity v≈0.15 t a, where a is the lattice spacing) that is absent when U=0. These parameters are chosen to be deep in the regime where the interaction-induced transfer of non-reciprocity dominates over direct bath effects on the uncoupled sector. We will also include a brief statement that the qualitative drift survives under moderate variations of U/t and γ/t, thereby establishing independence from the all-to-all solvability. revision: yes

Circularity Check

0 steps flagged

No circularity: exact solvability derived for specific model; generic claim rests on independent analysis of second model.

full rationale

The derivation begins with the definition of the all-to-all Hatsugai-Kohmoto Lindbladian, for which the paper states it establishes exact solvability via direct solution of the master equation. The directional-drift result in uncoupled sectors follows from that explicit solution. The extension to local interactions is performed on a separate driven-dissipative Fermi-Hubbard chain whose dynamics are analyzed independently (numerically or otherwise). No step equates a prediction to a fitted parameter by construction, renames a known result, or relies on a self-citation whose content is itself unverified. The central claims therefore remain self-contained against the paper's own equations and the additional model study.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the standard Lindblad formalism for open quantum systems and the choice of the Hatsugai-Kohmoto interaction for exact solvability; no free parameters or new entities are introduced in the abstract.

axioms (2)

standard math The dynamics of the open system are governed by a Lindblad master equation
Standard assumption in the field of open quantum systems.
domain assumption The Hatsugai-Kohmoto interaction allows exact solvability of the many-body Lindbladian
Specific model choice invoked to obtain closed-form dynamics.

pith-pipeline@v0.9.0 · 5476 in / 1409 out tokens · 58660 ms · 2026-05-10T16:58:18.189125+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Exact steady states of interacting driven dissipative fermionic systems with hidden time-reversal symmetry
quant-ph 2026-05 unverdicted novelty 7.0

Exact steady states are derived for interacting dissipative fermionic systems with hidden time-reversal symmetry, revealing a first-order particle density phase transition that survives finite dissipation.

Reference graph

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