Machine learning phases of matter
TL;DR: It is shown that modern machine learning architectures, such as fully connected and convolutional neural networks, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians.
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Abstract: The success of machine learning techniques in handling big data sets proves ideal for classifying condensed-matter phases and phase transitions. The technique is even amenable to detecting non-trivial states lacking in conventional order. Condensed-matter physics is the study of the collective behaviour of infinitely complex assemblies of electrons, nuclei, magnetic moments, atoms or qubits1. This complexity is reflected in the size of the state space, which grows exponentially with the number of particles, reminiscent of the ‘curse of dimensionality’ commonly encountered in machine learning2. Despite this curse, the machine learning community has developed techniques with remarkable abilities to recognize, classify, and characterize complex sets of data. Here, we show that modern machine learning architectures, such as fully connected and convolutional neural networks3, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians. Readily programmable through modern software libraries4,5, neural networks can be trained to detect multiple types of order parameter, as well as highly non-trivial states with no conventional order, directly from raw state configurations sampled with Monte Carlo6,7.
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Citations
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Dongil Shin,Andrea Cupertino,Matthijs H. J. de Jong,Peter G. Steeneken,Miguel A. Bessa,Richard A. Norte +5 more
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Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
Tomi Ohtsuki,Tomohiro Mano +1 more
TL;DR: In this article, the authors apply neural networks to condensed matter physics and obtain and represent the ground and excited state wave functions of the ground wave function of the wave function with a neural network.
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Mapping distinct phase transitions to a neural network.
TL;DR: It is demonstrated, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom.
Principal component analysis for fermionic critical points
Natanael C. Costa,Natanael C. Costa,Wenjian Hu,Zhaojun Bai,Richard T. Scalettar,Rajiv R. P. Singh +5 more
TL;DR: In this article, determinant quantum Monte Carlo (DQMC) was used to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials, including the zero-temperature antiferromagnet to singlet transition in the periodic Anderson model, the Mott insulating transition in Hubbard model on a honeycomb lattice, and the magnetic transition in 1/6-filled Lieb lattice.
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Unveiling phase transitions with machine learning
Askery Canabarro,Askery Canabarro,Felipe F. Fanchini,A. L. Malvezzi,Rodrigo G. Pereira,Rafael Chaves +5 more
TL;DR: It is shown how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase and it is shown that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neIGHbour interactions are introduced.
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