Application of Variational Autoencoder to Detect Critical Points of Anisotropic Classical Model*

The macroscopic properties of a physical system change at a phase transition. In most instances, the phase is identified using an order parameter consistent with the symmetry of the underlying Hamiltonian. We use recent advances in Machine Learning, in particular Autoencoders, to detect a phase transition just by identifying changes in the patterns of Quantum Monte Carlo data across the transition region, and without explicitly constructing any order parameter. We generalize previous studies on the application of variational autoencoders to the anisotropic two-dimensional Ising model. We identify the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Our phase diagram agrees with the one produced using the self-duality property of the model. Considering that the partition function of d + 1-dimensional anisotropic models can be mapped to that of the d-dimensional quantum spin models, this study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems.