SciPost Submission Page
Gauging the variational optimization of projected entangled-pair states
by Wei Tang, Laurens Vanderstraeten, Jutho Haegeman
Submission summary
| Authors (as registered SciPost users): | Wei Tang |
| Submission information | |
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| Preprint Link: | scipost_202510_00031v1 (pdf) |
| Data repository: | https://zenodo.org/records/16849083 |
| Date submitted: | Oct. 17, 2025, 10:30 p.m. |
| Submitted by: | Wei Tang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
I use generative AI tools to improve the grammar and fluency of my writing.
Abstract
Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for capturing ground state physics of two-dimensional quantum systems. However, accurately computing and minimizing the energy expectation value remains challenging, in part because the impact of the gauge degrees of freedom that are present in the tensor network representation is poorly understood. We analyze the role of gauge transformations for the case of a U(1)-symmetric PEPS with point group symmetry, thereby reducing the gauge degrees of freedom to a single class. We show how gradient-based optimization strategies exploit the gauge freedom, causing the tensor network contraction to become increasingly inaccurate and to produce artificially low variational energies. Furthermore, we develop a gauge-fixed optimization strategy that largely suppresses this effect, resulting in a more robust optimization. Our study underscores the need for gauge-aware optimization strategies to guarantee reliability of variational PEPS in general settings.
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
Report #1 by Anonymous (Referee 1) on 2025-11-18 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
Used Apple Intelligence to correct typos and to improve grammar.
Strengths
2-The explicit construction of gauge directions, the projection onto the tangent space, and the optimization of the manifold are technically sound.
3-The authors are very transparent about potential failures and do not conceal the instabilities within the MCF manifold when the search direction is distorted.
Weaknesses
1- Only one rather simple model is studied: a deep Mott insulator with a small D parameter and a tiny correlation length. While it would be interesting to consolidate the method by considering a more challenging model, the large numerical cost might make this very difficult.
2- No comparison with established optimization methods (imaginary-time / full update).
Report
Their proposed solution, constrained optimization using a minimal canonical form manifold with projected gradients, is simple and effective in the examined setting. Numerical evidence strongly supports the claim that gauge-aware optimization is more robust, producing physically meaningful tensors even when χ is small. The main limitations stem not from weaknesses in the method but from the narrowness of the test environment.
The study relies on a single model deep in a trivial phase and a symmetry structure that reduces gauge freedom to one dimension. Despite these limitations, the paper offers a significant and practical advance, providing a solid foundation for future work on gauge-aware PEPS optimization and identifying a clear direction for improving the reliability of tensor network methods.
Requested changes
1- If possible, include at least one test in a more entangled regime (larger correlation length, larger χ) to demonstrate robustness beyond the trivial case, e.g., pick a parameter near the Mott transition
2- If data is available, briefly compare to imaginary-time update methods to further demonstrated the importance of gauge-aware gradients.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)