Deep learning lattice gauge theories
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| author | Apte, Anuj Ashmore, Anthony Cordova, Clay Huang, Tzu-Chen |
| author_facet | Apte, Anuj Ashmore, Anthony Cordova, Clay Huang, Tzu-Chen |
| contents | Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep learning lattice gauge theories Apte, Anuj Ashmore, Anthony Cordova, Clay Huang, Tzu-Chen High Energy Physics - Lattice Disordered Systems and Neural Networks Strongly Correlated Electrons Machine Learning High Energy Physics - Theory Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory. |
| title | Deep learning lattice gauge theories |
| topic | High Energy Physics - Lattice Disordered Systems and Neural Networks Strongly Correlated Electrons Machine Learning High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.14830 |