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Abstract:The spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice exhibits a debated intermediate phase between Néel antiferromagnetic and stripe ordered regimes, with competing theories proposing plaquette valence bond, nematic, and quantum spin liquid ground states. We apply the Prometheus variational autoencoder framework -- previously applied to classical (2D, 3D Ising) and quantum (disordered transverse field Ising) phase transitions -- to systematically explore the $J_1$-$J_2$ phase diagram using a multi-scale approach. For $L=4$, we employ exact diagonalization with full wavefunction analysis via quantum-aware VAE. For larger systems ($L=6, 8$), we introduce a reduced density matrix (RDM) based methodology using DMRG ground states, enabling scaling beyond the exponential barrier of full Hilbert space representation. Through dense parameter scans of $J_2/J_1 \in [0, 1]$ and comprehensive latent space analysis, we identify the structure factor $S(\pi,\pi)$ and $S(\pi,0)$ as the dominant order parameters discovered by the VAE, with correlations exceeding $|r| > 0.97$. The RDM-VAE approach successfully captures the Néel-to-stripe crossover near $J_2/J_1 \approx 0.5$--$0.6$, demonstrating that local quantum correlations encoded in reduced density matrices contain sufficient information for unsupervised phase discovery. This work establishes a scalable pathway for applying machine learning to frustrated quantum systems where full wavefunction access is computationally prohibitive.
| Comments: | Substantial revision required across the whole text |
| Subjects: | Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2602.21468 [cond-mat.str-el] |
| (or arXiv:2602.21468v5 [cond-mat.str-el] for this version) | |
| https://doi.org/10.48550/arXiv.2602.21468 arXiv-issued DOI via DataCite |
From: Brandon Yee [view email]
[v1]
Wed, 25 Feb 2026 00:44:51 UTC (28 KB)
[v2]
Sat, 28 Feb 2026 02:36:00 UTC (36 KB)
[v3]
Wed, 11 Mar 2026 19:59:37 UTC (37 KB)
[v4]
Fri, 17 Apr 2026 21:53:34 UTC (38 KB)
[v5]
Fri, 24 Apr 2026 14:27:19 UTC (1 KB) (withdrawn)
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