Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function
Theoretical approaches to quantum many-body physics require developing compact representations of the complexity of generic quantum states. This paper explores an interpretable data-driven approach utilizing principal component analysis (PCA) and autoencoder neural networks to compress the two-parti...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ad9f20 |
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| author | Jiawei Zang Matija Medvidović Dominik Kiese Domenico Di Sante Anirvan M Sengupta Andrew J Millis |
| author_facet | Jiawei Zang Matija Medvidović Dominik Kiese Domenico Di Sante Anirvan M Sengupta Andrew J Millis |
| author_sort | Jiawei Zang |
| collection | DOAJ |
| description | Theoretical approaches to quantum many-body physics require developing compact representations of the complexity of generic quantum states. This paper explores an interpretable data-driven approach utilizing principal component analysis (PCA) and autoencoder neural networks to compress the two-particle vertex, a key element in Feynman diagram approaches. We show that the linear PCA offers more physical insight and better out-of-distribution generalization than the nominally more expressive autoencoders. Even with ∼10–20 principal components, we find excellent reconstruction across the phase diagram suggesting the existence of heretofore unrealized structures in the diagrammatic theory. We show that the principal components needed to describe the ferromagnetic state are not contained in the low rank description of the Fermi liquid (FL) state, unlike those for antiferromagnetic and superconducting states, suggesting that the latter two states emerge from pre-existing fluctuations in the FL while ferromagnetism is driven by a different process. |
| format | Article |
| id | doaj-art-07fbc196f2c24d76a7104bf2ed6cd3e5 |
| institution | DOAJ |
| issn | 2632-2153 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-07fbc196f2c24d76a7104bf2ed6cd3e52025-08-20T02:39:50ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015404507610.1088/2632-2153/ad9f20Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex functionJiawei Zang0https://orcid.org/0000-0002-3671-9282Matija Medvidović1Dominik Kiese2Domenico Di Sante3Anirvan M Sengupta4Andrew J Millis5Department of Physics, Columbia University , 538 W 120th Street, New York, NY 10027, United States of AmericaDepartment of Physics, Columbia University , 538 W 120th Street, New York, NY 10027, United States of America; Center for Computational Quantum Physics, Flatiron Institute , 162 5th Avenue, New York, NY 10010, United States of AmericaCenter for Computational Quantum Physics, Flatiron Institute , 162 5th Avenue, New York, NY 10010, United States of AmericaDepartment of Physics and Astronomy, Alma Mater Studiorum—University of Bologna , Bologna 40127, ItalyCenter for Computational Quantum Physics, Flatiron Institute , 162 5th Avenue, New York, NY 10010, United States of America; Department of Physics and Astronomy, Rutgers University , 136 Frelinghuysen Road, Piscataway, NJ 08854, United States of America; Center for Computational Mathematics, Flatiron Institute , 162 5th Avenue, New York, NY 10010, United States of AmericaDepartment of Physics, Columbia University , 538 W 120th Street, New York, NY 10027, United States of America; Center for Computational Quantum Physics, Flatiron Institute , 162 5th Avenue, New York, NY 10010, United States of AmericaTheoretical approaches to quantum many-body physics require developing compact representations of the complexity of generic quantum states. This paper explores an interpretable data-driven approach utilizing principal component analysis (PCA) and autoencoder neural networks to compress the two-particle vertex, a key element in Feynman diagram approaches. We show that the linear PCA offers more physical insight and better out-of-distribution generalization than the nominally more expressive autoencoders. Even with ∼10–20 principal components, we find excellent reconstruction across the phase diagram suggesting the existence of heretofore unrealized structures in the diagrammatic theory. We show that the principal components needed to describe the ferromagnetic state are not contained in the low rank description of the Fermi liquid (FL) state, unlike those for antiferromagnetic and superconducting states, suggesting that the latter two states emerge from pre-existing fluctuations in the FL while ferromagnetism is driven by a different process.https://doi.org/10.1088/2632-2153/ad9f20deep learningmachine learningquantum systemmany-body system |
| spellingShingle | Jiawei Zang Matija Medvidović Dominik Kiese Domenico Di Sante Anirvan M Sengupta Andrew J Millis Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function Machine Learning: Science and Technology deep learning machine learning quantum system many-body system |
| title | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| title_full | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| title_fullStr | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| title_full_unstemmed | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| title_short | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| title_sort | machine learning based compression of quantum many body physics pca and autoencoder representation of the vertex function |
| topic | deep learning machine learning quantum system many-body system |
| url | https://doi.org/10.1088/2632-2153/ad9f20 |
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