Classification of nodal pockets in many-electron wave functions via machine learning

LeDell, Erin; Prabhat,; Zubarev, Dmitry Yu.; Austin, Brian; Lester, William A.

doi:10.1007/s10910-012-0019-5

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…In the last years physicists started to employ machine learning techniques. Most of the tasks were tackled by supervised learning algorithms or with the help of reinforcement learning [10][11][12][13][14][15][16][17][18][19][20][21][22]. Supervised learning means one is given labeled training data from which the algorithm learns to assign labels to data points.…”

Section: Introductionmentioning

confidence: 99%

Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

2017

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We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to artificial neural network based variational autoencoders. The states are sampled using a Monte-Carlo simulation above and below the critical temperature. We find that the predicted latent parameters correspond to the known order parameters. The latent representation of the states of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence or the underlying Hamiltonian. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.

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Section: Introductionmentioning

confidence: 99%

Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

2017

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“…Meanwhile, Broecker etal 15 have also used DQMC for the Hubbard model together with CNN with a focus on understanding if the sign problem can be circumvented. Learning about the sign problem is also implicit in machine learning studies of the nodal surfaces of many-electron wave functions 16 . A particularly intriguing proposal uses a machine-learned effective bosonic action to guide proposed moves at a much lower cost than the usual cube of the system size [17][18][19] .…”

Section: Introductionmentioning

confidence: 99%

Principal component analysis for fermionic critical points

Costa

Bai

et al. 2017

Phys. Rev. B

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We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature CDW transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom. We examine the different behaviors associated with providing Hubbard-Stratonovich auxiliary fields configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

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“…These new developments call for new ways of identifying appropriate indicators of phase transitions.To meet this challenge, we use machine learning techniques to extract information of phases and phase transitions directly from many-body configurations. In fact, application of machine learning techniques to condensed matter physics is a burgeoning field [3][4][5][6][7][8][9][10][11][12][13][33]. For example, regression approaches are used to predict crystal structures [3], to approximate density functionals [6], and to solve quantum impurity problems [10]; artificial neural networks are trained to classify phases of classical statistical models [13].…”

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confidence: 99%

Discovering phase transitions with unsupervised learning

2016

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Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low dimensional representations the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds out physical concepts such as order parameter and structure factor to be indicators of the phase transition. We discuss future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.Classifying phases of matter and identifying phase transitions between them is one of the central topics of condensed matter physics research. Despite an astronomical number of constituting particles, it often suffices to represent states of a many-body system with only a few variables. For example, a conventional approach in condensed matter physics is to identify order parameters via symmetry consideration or analyzing low energy collective degree of freedoms and use them to label phases of matter [1].However, it is harder to identify phases and phase transitions in this way in an increasing number of new states of matter, where the order parameter may only be defined in an elusive nonlocal way [2]. These new developments call for new ways of identifying appropriate indicators of phase transitions.To meet this challenge, we use machine learning techniques to extract information of phases and phase transitions directly from many-body configurations. In fact, application of machine learning techniques to condensed matter physics is a burgeoning field [3][4][5][6][7][8][9][10][11][12][13][33]. For example, regression approaches are used to predict crystal structures [3], to approximate density functionals [6], and to solve quantum impurity problems [10]; artificial neural networks are trained to classify phases of classical statistical models [13]. However, most of those applications use supervised learning techniques (regression and classification), where a learner needs to be trained with the previously solved data set (input/output pairs) before it can be used to make predictions.On the other hand, in the unsupervised learning, there is no such explicit training phase. The learner should by itself find out interesting patterns in the input data. Typical unsupervised learning tasks include cluster analysis and feature extraction. Cluster analysis divides the input data into several groups based on certain measures of similarities. Feature extraction finds a low-dimensional representation of the dataset while still preserving essential characteristics of the original data. Unsupervised learning methods have broad applications in data compression, visualization, online advertising and reco...

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Classification of nodal pockets in many-electron wave functions via machine learning

Cited by 5 publications

References 17 publications

Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

Principal component analysis for fermionic critical points

Discovering phase transitions with unsupervised learning

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