From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

Abstract

We extend the Prometheus framework for unsupervised phase transition discovery from 2D classical systems to 3D classical and quantum many-body systems, addressing scalability in higher dimensions and generalization to quantum fluctuations. For the 3D Ising model (L 32), the framework detects the critical temperature within 0.01\% of literature values (T_c/J = 4.511 0.005) and extracts critical exponents with 70\% accuracy (β= 0.328 0.015, γ= 1.24 0.06, ν= 0.632 0.025), correctly identifying the 3D Ising universality class via χ^2 comparison (p = 0.72) without analytical guidance. For quantum systems, we developed quantum-aware VAE (Q-VAE) architectures using complex-valued wavefunctions and fidelity-based loss. Applied to the transverse field Ising model, we achieve 2\% accuracy in quantum critical point detection (h_c/J = 1.00 0.02) and successfully discover ground state magnetization as the order parameter (r = 0.97). Notably, for the disordered transverse field Ising model, we detect exotic infinite-randomness criticality characterized by activated dynamical scaling ξ |h - h_c|^-ψ, extracting a tunneling exponent ψ= 0.48 0.08 consistent with theoretical predictions (ψ= 0.5). This demonstrates that unsupervised learning can identify qualitatively different types of critical behavior, not just locate critical points. Our systematic validation across classical thermal transitions (T = 0 to T > 0) and quantum phase transitions (T = 0, varying h) establishes that VAE-based discovery generalizes across fundamentally different physical domains, providing robust tools for exploring phase diagrams where analytical solutions are unavailable.

Reproductions