SciPost Submission Page
A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains
by Ken Inayoshi, Maksymilian Środa, Anna Kauch, Philipp Werner, Hiroshi Shinaoka
Submission summary
| Authors (as registered SciPost users): | Ken Inayoshi · Maksymilian Środa |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2509.15028v3 (pdf) |
| Date accepted: | Feb. 9, 2026 |
| Date submitted: | Dec. 23, 2025, 4:33 a.m. |
| Submitted by: | Ken Inayoshi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
In the main text, GitHub Copilot in VS Code (ChatGPT-4.1) was used for spelling and grammar checking.
Abstract
We propose a causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains. This algorithm enables stable and efficient extensions of the simulated time domain by exploiting the causality of Green's functions. We apply this approach within the framework of nonequilibrium dynamical mean-field theory to the simulation of quench dynamics in symmetry-broken phases, where long-time simulations are often required to capture slow relaxation dynamics. We demonstrate that our algorithm allows to extend the simulated time domain without a significant increase in the cost of storing the Green's function.
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
List of changes
We thank the editors for sending us the referee reports and two referees for their careful comments. Following the suggestions of the referees, we have made the following changes to the manuscript.
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At the end of the first paragraph of the Introduction section, we have added an explanation of how the memory and computational costs scale with the number of momentum points.
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In the final paragraph of Sec. 2.1, we have clarified the data size in the original representation of the Green’s function.
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In the second to last paragraph of Sec. 5.2.2, we have included a discussion of the runtime memory and computational costs of both the conventional method and our QTT method. To consolidate the discussion, we moved the relevant text originally located in the paragraph starting with ”Figure 9 compares...” to this paragraph.
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In the second to last paragraph of the Conclusion section, we have extended the discussion on preparing the initial guess of the Green’s function via the dynamic mode decomposition, as proposed in our parallel work (arXiv:2509.22177).
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In the final paragraph of the Conclusion section, we have added a discussion of future directions for applying the QTT method to more realistic ab initio simulations.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report
I recommend the paper for publication.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Strengths
- This paper improves a previous method of finding non-equilibrium Green’s functions with Quantics Tensor Trains by using a causality-based divide and conquer algorithms, which in practice corresponds in solving the Green’s function globally for a given time tmax and then fixing the Green’s function inside this time domain and increase the time domain slower Δt and just update the part of the Green’s function corresponding to this Δt.
- They use this method to find the non-equilibrium DMFT Green’s functions of the Hubbard model in the AFM phase and compare their results with the conventional approach implemented with NESSi.
- They compare the data-size of the Green’s functions found by conventional methods and those found with QTT methods, finding an improvement of almost 3 orders of magnitude when compressing the data with QTT.
Report
All in all, I would recommend this paper for publication after a couple of minor issues are addressed.
Requested changes
All the requested changes have been made
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)