Detecting composite orders in layered models via machine learning

Abstract

We use machine learning to study layered spin models where composite order parameters may emerge as a consequence of the interlayerer coupling. We focus on the layered Ising and Ashkin-Teller models, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find.

Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning

“…for fermionic theories in [7,11]. The approach also enables novel procedures, such as learning by confusion and similar techniques, to locate phase transitions in a semi-supervised manner [15,34]. For lattice QCD, action parameters can be extracted from field configurations [24].…”

Machine learning effective models for quantum systems

“…However, mapping the input to the desired output in deep learning by processing through successive layers of ever increasing abstraction is conceptually similar to RG [12][13][14][15][16][17]. Applications of ML in physics include the search for eigenstates of Hamiltonians [18][19][20][21][22][23], the inverse problem of finding the parent Hamiltonian of a given state [24][25][26], predicting properties of materials [27,28], and identifying phases of matter [29][30][31][32]. In our model ML approach, the optimized probabilistic model is the desired effective model, and has physical meaning.…”