Trapped Fermions Through Kolmogorov-Arnold Wavefunctions
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912754367987712 |
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| author | Bedaque, Paulo F. Cigliano, Jacob Kumar, Hersh Paul, Srijit Rajawat, Suryansh |
| author_facet | Bedaque, Paulo F. Cigliano, Jacob Kumar, Hersh Paul, Srijit Rajawat, Suryansh |
| contents | We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-$\frac{1}{2}$ fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ansätze. The method can, in principle, achieve arbitrary accuracy, limited only by the Monte Carlo sampling and was checked against exact results at sub-percent precision. For attractive interactions, it captures pairing effects, and in the impurity case it agrees with known results. We present a method of systematic transfer learning in the number of network parameters, allowing for efficient training for a target precision. We vastly increase the efficiency of the method by incorporating the short-distance behavior of the wavefunction into the ansätz without biasing the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trapped Fermions Through Kolmogorov-Arnold Wavefunctions Bedaque, Paulo F. Cigliano, Jacob Kumar, Hersh Paul, Srijit Rajawat, Suryansh Nuclear Theory Disordered Systems and Neural Networks Quantum Gases Computational Physics Quantum Physics We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-$\frac{1}{2}$ fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ansätze. The method can, in principle, achieve arbitrary accuracy, limited only by the Monte Carlo sampling and was checked against exact results at sub-percent precision. For attractive interactions, it captures pairing effects, and in the impurity case it agrees with known results. We present a method of systematic transfer learning in the number of network parameters, allowing for efficient training for a target precision. We vastly increase the efficiency of the method by incorporating the short-distance behavior of the wavefunction into the ansätz without biasing the method. |
| title | Trapped Fermions Through Kolmogorov-Arnold Wavefunctions |
| topic | Nuclear Theory Disordered Systems and Neural Networks Quantum Gases Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.07800 |