Machine learning quantum phases of matter beyond the fermion sign problem

Broecker, Peter; Carrasquilla, Juan; Melko, Roger G.; Trebst, Simon

doi:10.1038/s41598-017-09098-0

Cited by 379 publications

(315 citation statements)

References 51 publications

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“…Here, V (2,1) is a n 2 × n 1 matrix, and matrix-vector multiplication between V (2,1) and x is implied here as well as below. Each entry of the resulting vector x (2) can be interpreted as the output of an individual neuron, of which there are n 2 in total. In general, the first layer is followed by further layers, each of which implements the map…”

Section: Neural Network For Binary Classificationmentioning

confidence: 99%

“…In the first layer, the input vectors x of dimension n 1 are mapped to a space of dimension n 2 via an affine linear map x → V (2,1) x + a (2) , followed by the application of a nonlinear activation function g 2 (the nonlinearity of which is required in order to be able to approximate arbitrary maps f ), so that the full action of the first layer may be written as (2) ). Here, V (2,1) is a n 2 × n 1 matrix, and matrix-vector multiplication between V (2,1) and x is implied here as well as below.…”

Section: Neural Network For Binary Classificationmentioning

confidence: 99%

“…In physics, the application of neural networks, and machine learning in general, to many-body quantum mechanics is a novel and burgeoning field of research [1]. Currently, there are three main lines of pursuit: the application of machine learning to the problem of classifying various phases of matter [2][3][4][5][6][7][8][9], accelerating material searches and design [10][11][12][13], and the quest to encode quantum mechanical states in structures mimicking the setup of a neural network [14][15][16]. This work is concerned with the first kind of approach.…”

Section: Introductionmentioning

confidence: 99%

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Probing many-body localization with neural networks

2017

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We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.

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Section: Neural Network For Binary Classificationmentioning

confidence: 99%

Section: Neural Network For Binary Classificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probing many-body localization with neural networks

2017

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“…Machine learning is emerging as a novel tool for identifying phases of matter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. At its core, this problem can be cast as a classification problem in which data obtained from physical systems are assigned a class (i.e., a phase) using machine learning methods.…”

mentioning

confidence: 99%

“…At its core, this problem can be cast as a classification problem in which data obtained from physical systems are assigned a class (i.e., a phase) using machine learning methods. This approach has enabled the autonomous detection of order parameters [2,5,6], phase transitions [1,3], and entire phase diagrams [4,7,16,17]. Simultaneous research effort at the interface between machine learning and many-body physics has focused on the use of neural networks for efficient representations of quantum wave functions [18][19][20][21][22][23][24][25][26], drawing a parallel between deep networks and the renormalization group [27][28][29].…”

mentioning

confidence: 99%

Learning phase transitions from dynamics

2018

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We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two distinct models of one-dimensional disordered and interacting spin chains. The obtained phase diagram for a well-studied model of the many-body localization transition shows excellent agreement with previously known results obtained from time-independent entanglement spectra. For a periodically driven model featuring an inherently dynamical time-crystalline phase, the phase diagram that our network traces coincides with an order parameter for its expected phases.

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On the application of machine learning in astronomy and astrophysics: A text‐mining‐based scientometric analysis

Rodríguez

Rodríguez‐Rodríguez

Woo

2022

WIREs Data Min & Knowl

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Since the beginning of the 21st century, the fields of astronomy and astrophysics have experienced significant growth at observational and computational levels, leading to the acquisition of increasingly huge volumes of data. In order to process this vast quantity of information, artificial intelligence (AI) techniques are being combined with data mining to detect patterns with the aim of modeling, classifying or predicting the behavior of certain astronomical phenomena or objects. Parallel to the exponential development of the aforementioned techniques, the scientific output related to the application of AI and machine learning (ML) in astronomy and astrophysics has also experienced considerable growth in recent years. Therefore, the increasingly abundant articles make it difficult to monitor this field in terms of which research topics are the most prolific or novel, or which countries or authors are leading them. In this article, a text‐mining‐based scientometric analysis of scientific documents published over the last three decades on the application of AI and ML in the fields of astronomy and astrophysics is presented. The VOSviewer software and data from the Web of Science (WoS) are used to elucidate the evolution of publications in this research field, their distribution by country (including co‐authorship), the most relevant topics addressed, and the most cited elements and most significant co‐citations according to publication source and authorship. The obtained results demonstrate how application of AI/ML to the fields of astronomy/astrophysics represents an established and rapidly growing field of research that is crucial to obtaining scientific understanding of the universe. This article is categorized under: Algorithmic Development > Text Mining Technologies > Machine Learning Application Areas > Science and Technology

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Machine learning quantum phases of matter beyond the fermion sign problem

Cited by 379 publications

References 51 publications

Probing many-body localization with neural networks

Probing many-body localization with neural networks

Learning phase transitions from dynamics

On the application of machine learning in astronomy and astrophysics: A text‐mining‐based scientometric analysis

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