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Identifying Quantum Phase Transitions with Minimal Prior Knowledge by Unsupervised Learning
by Mohamad Ali Marashli, Ho Lai Henry Lam, Hamam Mokayed, Fredrik Sandin, Marcus Liwicki, Ho-Kin Tang, Wing Chi Yu
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Submission summary
| Authors (as registered SciPost users): | Wing Chi Yu |
| Submission information | |
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| Preprint Link: | scipost_202409_00005v2 (pdf) |
| Date accepted: | 2025-02-11 |
| Date submitted: | 2025-01-16 11:17 |
| Submitted by: | Yu, Wing Chi |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
In this work, we proposed a novel approach for identifying quantum phase transitions in one-dimensional quantum many-body systems using AutoEncoder (AE), an unsupervised machine learning technique, with minimal prior knowledge. The training of the AEs is done with reduced density matrix (RDM) data obtained by Exact Diagonalization (ED) across the entire range of the driving parameter and thus no prior knowledge of the phase diagram is required. With this method, we successfully detect the phase transitions in a wide range of models with multiple phase transitions of different types, including the topological and the Berezinskii-Kosterlitz-Thouless transitions by tracking the changes in the reconstruction loss of the AE. The learned representation of the AE is used to characterize the physical phenomena underlying different quantum phases. Our methodology demonstrates a new approach to studying quantum phase transitions with minimal knowledge, small amount of needed data, and produces compressed representations of the quantum states.
Author comments upon resubmission
List of changes
1. Lines 124-125, added comments about RDM sparsity effect in learning compressed embedding.
2. Fig. 3 caption, added clarification that entanglement spectrum is used as input
3. Fig.4 , replace old graph with corrected new one
4. Lines 208-211, addressed the disadvantage of increased input dimension due to changing input from ES to RDM
5. Lines 213,232,314 : specified the input and embedding dimensions of the data.
6. Fig. 5 c, added inset showing the XY-LargeD transition
7. Lines 241-243 : added possible explanation of Haldane phase transitions result deviation from reference.
8. Lines 262-264, Fig. 7 caption , added explanation of the visualization seen in Fig. 7
9. Added Fig. 9 to show XY1-XY2 transition.
10. Added Fig.11 to show SSH loss and explain the ‘peak’, ‘valley’ in Fig. 10
11. Added Fig.12 to show PS phase transitions.
12. Modified the conclusion, replacing studying higher dimensions system in future works to modifying method to work on block RDM obtained from DMRG simulations
13. Added appendix B to show effect of training region
14. Added appendix D to show effect of shortcut connection
Published as SciPost Phys. Core 8, 029 (2025)
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The authors have replied to my comments, nonetheless I have a remark to make regarding R2.
Fig. 3.b) shows that the system, at the given N=20 size, has the transition at Delta = +1, so when you don't see the transition here, it's doesn't seem to be a finite size effect of the system. There could be a finite size effect of your AE. You showed in the new Fig. 15 that your transition points are strongly affected by the shortcut (which is quite surprising to me). Then I think it's expected for your transition points to improve if you make your network larger and better performing. This should be emphasized.
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