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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2403.15372 |
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| _version_ | 1866916172438437888 |
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| author | Zang, Jiawei Medvidović, Matija Kiese, Dominik Di Sante, Domenico Sengupta, Anirvan M. Millis, Andrew J. |
| author_facet | Zang, Jiawei Medvidović, Matija Kiese, Dominik Di Sante, Domenico Sengupta, Anirvan M. Millis, Andrew J. |
| contents | Characterizing complex many-body phases of matter has been a central question in quantum physics for decades. Numerical methods built around approximations of the renormalization group (RG) flow equations have offered reliable and systematically improvable answers to the initial question -- what simple physics drives quantum order and disorder? The flow equations are a very high dimensional set of coupled nonlinear equations whose solution is the two particle vertex function, a function of three continuous momenta that describes particle-particle scattering and encodes much of the low energy physics including whether the system exhibits various forms of long ranged order. In this work, we take a simple and interpretable data-driven approach to the open question of compressing the two-particle vertex. We use PCA and an autoencoder neural network to derive compact, low-dimensional representations of underlying physics for the case of interacting fermions on a lattice. We quantify errors in the representations by multiple metrics and show that a simple linear PCA offers more physical insight and better out-of-distribution (zero-shot) generalization than the nominally more expressive nonlinear models. Even with a modest number of principal components (10 - 20), we find excellent reconstruction of vertex functions across the phase diagram. This result suggests that many other many-body functions may be similarly compressible, potentially allowing for efficient computation of observables. Finally, we identify principal component subspaces that are shared between known phases, offering new physical insight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function Zang, Jiawei Medvidović, Matija Kiese, Dominik Di Sante, Domenico Sengupta, Anirvan M. Millis, Andrew J. Strongly Correlated Electrons Characterizing complex many-body phases of matter has been a central question in quantum physics for decades. Numerical methods built around approximations of the renormalization group (RG) flow equations have offered reliable and systematically improvable answers to the initial question -- what simple physics drives quantum order and disorder? The flow equations are a very high dimensional set of coupled nonlinear equations whose solution is the two particle vertex function, a function of three continuous momenta that describes particle-particle scattering and encodes much of the low energy physics including whether the system exhibits various forms of long ranged order. In this work, we take a simple and interpretable data-driven approach to the open question of compressing the two-particle vertex. We use PCA and an autoencoder neural network to derive compact, low-dimensional representations of underlying physics for the case of interacting fermions on a lattice. We quantify errors in the representations by multiple metrics and show that a simple linear PCA offers more physical insight and better out-of-distribution (zero-shot) generalization than the nominally more expressive nonlinear models. Even with a modest number of principal components (10 - 20), we find excellent reconstruction of vertex functions across the phase diagram. This result suggests that many other many-body functions may be similarly compressible, potentially allowing for efficient computation of observables. Finally, we identify principal component subspaces that are shared between known phases, offering new physical insight. |
| title | Machine learning-based compression of quantum many body physics: PCA and autoencoder representation of the vertex function |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.15372 |