Remote spin control in Haldane spin chains

1) Very simple methodology.

2) Straightforward interpretation.

I read the paper with interest. The authors discuss the application of a magnetic field sweep at the edge of a spin chain in what they call the "Haldane phase" and how the sweep affects the magnetization along the chain.

Due to the fact that the spin chain display a singlet ground state with an exponentially small gap from a triplet state, the entire dynamics can be understood in terms of a Landau-Zener model involving only this 4 low lying states.

The paper is stylistically polished and it is written in such a way that it makes a very clear and comprehensible story. Unfortunately, the narrative and the well articulated connections with experimentals platforms remains the main strength of the paper, which, as a theoretical analysis, is not particularly deep or surprising.

The entire analysis rests only on the solution fo the Landau-Zener problem, since the original 4 level systems effectively decouples to a two level system. This problem is well known and its solution has been applied to countless physics problems. So, the methodology does not present particular novelty.

However, it is not just a question of simplicity of the methodology. The entire theoretical analysis appears very straightforward. As the authors argue, the fact that the edge modes are coupled for any finite chain makes the possibility to influence one edge by acting on the other one rather straightforward.

Indeed, the entire magnetization of the chain is effected by the manipulation of the edge, but even this is rather obvious. This is a slow, low-energy, dynamics and only considers the tunneling between ground-state and first excited states. These are thermodynamic configurations and their magnetization profile is clearly effected by the boundary conditions so that changing the boundary conditions (which is the same as modifying the magnetic field at the edge) obviously affects the entire chain.

The authors wants to argue that this constitutes a form of "action at a distance" since the two edges are far apart, but this fact is rather standard for a coherent quantum systems in the slow drive limit. In fact as the size of the system is increased one needs to have a increasingly slow rate since the system needs more time to "adjust" to the new configuration and remain in the low energy sector. In this definition, the larger the distance, the more time you need to wait to transfer the information and, therefore, I would not talk of action at a distance.

In summary, I do not find the paper very innovative nor based on the results or the methodology. However, I do find the presentation worthwhile and the connection with experimental platforms may offer some interesting perspectives for the specialist in the field.

I recommend the publication of the paper on Scipost Core.

The authors may need to revise the stile of the paper. They often use >> or << rather than the specific command \ll and \gg (probably a problem of using AI).

Also, they should properly comment the figure to discuss the meaning of the colored curves.

Accept in alternative Journal (see Report)

This manuscript describes the effects of a magnetic field applied to one edge of an Haldane chain and demonstrates that such a magnetic field affects the opposite edge significantly. The reason of this effect is that the edges of an Haldane chain host two quasi-degenerate spin-1/2 excitations, coupled by a weak Heisenberg coupling whose intensity decreases exponentially with system size. The authors describe an experimental realization using nanographene spin chains, Ref. [20].

The physics described in this article is easily understood in terms of a 2-qubit Hamiltonian and is not peculiar to Haldane chains. For example, I think that one could obtain a similar effect by considering a 1d Bose-Hubbard model with 2 particles and applying a negative chemical potential at the two edges. The super-exchange between the edges would give rise to a coupling very similar to the one considered here and is not related to the topological properties of the Heisenberg chain.

In my opinion, this work does not constitute a "new direction of research", nor a "groundbreaking discovery". I recommend resubmitting this work to a less selective journal, after having addressed the comments below.

MAJOR REMARKS

1. The authors refer to the edge states of the Haldane chain as "fractionalized". While this is correct in the case of the spin-1 Heisenberg model, the natural charges of the AEHM are already spin-1/2 and no fractionalization occurs.

2. The authors refer to the observed effect as "non-local". In the context of topological phases, this term has a special meaning and should not be applied to an effect controlled by an coupling that decreases exponentially with the system size, unless explicitly mentioning this distinction.

MINOR REMARKS: 3. "<<" instead of "\ll" in several occasions.

1. Page 3. What is "Nmax"?

2. Page 4. "so that ... so that"

3. Page 4. "The discussion that follows would be the same if". Presumably one would need to perform a different calculation.

Reject