SciPost Submission Page
Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
by Adam J. McRoberts, Roderich Moessner
Submission summary
| Authors (as registered SciPost users): | Adam McRoberts |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2407.13816v2 (pdf) |
| Date submitted: | 2024-08-13 12:09 |
| Submitted by: | McRoberts, Adam |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Motivated by recent experiments on Google's sycamore NISQ platform on the spin transport resulting from a non-unitary periodic boundary drive of an XXZ chain, we study a classical variant thereof by a combination of analytical and numerical means. We find the classical model reproduces the quantum results in remarkable detail, and provides an analytical handle on the nature and shape of the spin transport's three distinct regimes: ballistic (easy-plane), subdiffusive (isotropic) and insulating (easy-axis). Further, we show that this phenomenology is remarkably robust to the inclusion of bond disorder -- albeit that the transient dynamics approaching the steady states differs qualitatively between the clean and disordered cases -- providing an accessible instance of ballistic transport in a disordered setting.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1 - study of a topical experiment/simulation in a NISQ computer
2- unusual result of persistence of ballistic transport in the presence of disorder
Weaknesses
1 - model could be explained in more detail
Report
The authors study both analytically and numerically a recent experiment by Google simulating a boundary driven XXZ spin chain. They focus on the classical, large S, limit and find good agreement with experiment. A very interesting result is their finding of persistence of ballistic transport even in the presence of disorder in the easy plane regime. This stability is because the disorder cannot modify the consistency equation significantly. This is an important point.
Requested changes
1 - the model is not very clear. I only understand what the driving was when I read the caption of Fig. 1. They do discuss it later around Eq. (6), but I suggest that the authors discuss this in more detail and earlier in the text (around Eq. (1)).
2- The discussion about why the ballistic transport is stable to disorder is too short in my opinion. In fact, most of it is in Appendix C. I would suggest expanding this discussion with perhaps an analytical and numerical example to clarify.
Recommendation
Ask for minor revision
Strengths
- timely topic, directly relevant for experiments
- interesting results, and nice analytical derivation of the non-equilibrium steady state and on the stability of the ballistic transport
Weaknesses
- some results were already derived in previous papers
- the quantum-classical correspondence, and especially the role of integrability, is not really explained
Report
As mentioned above, the paper is very fascinating as it shows that the classical Heisenberg chain captures most of the features observed in the boundary driven XXZ chain. The calculations are correct, and the numerical simulations are high quality. The paper deserves publication.
As mentioned above, however, the paper would be of much better quality if the quantum-classical correspondence, and the role of integrability, is better explained. Currently, it mostly looks like a coincidence. We know indeed (for example for the problem of the domain wall of spins or the superdiffusive transport) that there exists some kind of universality class of spin transport given by the classical, integrable, Landau–Lifshitz. The latter can be discretized giving an integrable classical spin chain (also it can be trotterised, see the works in the Prosen group). The authors could run some numerics with the integrable model, showing that the same behavior is observed, or not. This would clarify if the phenomena at hand are actually, also in this case, due to the Landau–Lifshitz equation.
Requested changes
see above.
Recommendation
Publish (meets expectations and criteria for this Journal)