Simulating the Hubbard Model with Equivariant Normalizing Flows
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913646469185536 |
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| author | Schuh, Dominic Kreit, Janik Berkowitz, Evan Funcke, Lena Luu, Thomas Nicoli, Kim A. Rodekamp, Marcel |
| author_facet | Schuh, Dominic Kreit, Janik Berkowitz, Evan Funcke, Lena Luu, Thomas Nicoli, Kim A. Rodekamp, Marcel |
| contents | Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations.
In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulating the Hubbard Model with Equivariant Normalizing Flows Schuh, Dominic Kreit, Janik Berkowitz, Evan Funcke, Lena Luu, Thomas Nicoli, Kim A. Rodekamp, Marcel Strongly Correlated Electrons Machine Learning High Energy Physics - Lattice Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations. In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues. |
| title | Simulating the Hubbard Model with Equivariant Normalizing Flows |
| topic | Strongly Correlated Electrons Machine Learning High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2501.07371 |