Unsupervised Discovery of Intermediate Phase Order in the Frustrated J_1-J_2 Heisenberg Model via Prometheus Framework

arXiv:2602.21468v4 Announce Type: replace-cross Abstract: The spin-1/2 J_1-J_2 Heisenberg model on the square lattice exhibits a debated intermediate phase between Neel 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 Neel-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.

Source: arXiv cs.LG | 2026-04-21