Unsupervised learning of phase transition in quantum spin model

Abstract

This report investigates the application of unsupervised learning techniques to detect phase transitions in quantum spin systems, focusing on the 2D and 3D Ising models. Using Monte Carlo simulations, we generate spin configurations and apply Principal Component Analysis (PCA), autoencoders, and Variational Autoencoders (VAEs) to identify critical temperatures. For the 2D Ising model, PCA estimates Tc ≈ 2.25J/kB across varying lattice sizes with no external field, while autoencoders and VAEs detect Tc ≈ 2.3J/kB for a 45×45 lattice, aligning closely with the theoretical value of 2.269J/kB. In the 3D Ising model (L = 10), VAEs pinpoint Tc ≈ 4.5kT, consistent with established results. These methods effectively capture linear and nonlinear features of phase transitions, with VAEs offering enhanced latent space interpretability. Our findings highlight unsupervised learning’s potential as a scalable tool for studying complex quantum systems, suggesting future applications to models like the Heisenberg model.