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Lecture notes in computer science

Deep Machine Learning Investigation of Phase Transitions

Vladislav Chertenkov, Evgeni Burovski, Щур Лев Николаевич

Published Jan 1, 2022• 3 citations
Publisher
DOI
10.1007/978-3-031-22941-1_29

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•Sep 6, 2019•5 citations
We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin configurations using known values of disordered phase energy and ordered phase energy. The trained neural network is used to predict whether a given sample belong to one or another phase of matter. This allows us to estimate for the first time the probability that configurations with a certain energy belong to the ordered phase, coexistence phase, and disordered phase. Based on these probabilities, we obtained estimates of the values of the critical energies and latent heat for the Potts model with 10 and 20 components, which undergoes a strong discontinuous transition. We also found that the probabilities may reflect geometric transitions in the coexistence phase.
This paper investigates the use of autoencoders and machine learning methods for detecting and analyzing quantum phase transitions in the Two-Component Bose-Hubbard Model. By leveraging deep learning models such as autoencoders, we investigate latent space representations, reconstruction error analysis, and cluster distance calculations to identify phase boundaries and critical points. The study is supplemented by dimensionality reduction techniques such as PCA and t-SNE for latent space visualization. The results demonstrate the potential of autoencoders to describe the dynamics of quantum phase transitions.
In the past years Machine Learning has shown to be a useful tool in quantum many-body physics to detect phase transitions. Being able to identify phases via machine learning introduces the question of how did the algorithm learn to classify them, and thus how to interpret the model?s prediction. In this thesis we present a study of the transition from a normal insulator to a topological insulator. We study this quantum phase transition in the framework of the Su-Schrie?er-Heeger model. In the area of Deep Learning, we introduce two models, a normal convolutional neural network and a model based on deep residual learning. In particular, we focus on the interpretability of the model and its prediction by generating class activation maps (CAM) using a global average pooling (GAP) layer. We show the application of this technique by applying it on the model without disorder and with disorder. Here we give further analysis of the detection of states using transfer learning from no disordered to disordered systems. We conclude that the neural network is able to detect edge states when there is no disorder but unable to distinguish between edge states and Anderson localized states when disorder is introduced.