Abstract
Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems.
Highlights
The various modern architectures of neural networks consisting of multiple layers and neuron types can be trained to classify, with a high degree of accuracy, intricate sets of labeled data [1]
We show that a threedimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one
The approximately 80 000 labeled configurations at various temperatures around TN are generated through determinantal quantum Monte Carlo (DQMC) simulations for two interaction strengths, U 1⁄4 5 and 16, one in the weak-coupling and one in the strong-coupling regime, and shuffled before they are used in the training
Summary
The various modern architectures of neural networks consisting of multiple layers and neuron types (see Fig. 1 for an example) can be trained to classify, with a high degree of accuracy, intricate sets of labeled data [1]. Common to most algorithms involving neural networks is the training procedure, which is an optimization problem where the free parameters associated with connections between neurons in adjacent layers and their biases (additive constants) are slowly adjusted until a high classification accuracy is attained. Embodied in the study of quantum and classical statistical mechanics are the manybody states, which can be understood as immense data sets associated with the equilibrium state of the system, and over which machine learning techniques can be naturally applied.
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