Variational Neural and Tensor Network Approximations of Thermal States
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910832034578432 |
|---|---|
| author | Lu, Sirui Giudice, Giacomo Cirac, J. Ignacio |
| author_facet | Lu, Sirui Giudice, Giacomo Cirac, J. Ignacio |
| contents | We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the ansatz expressiveness without accumulating errors from iterative imaginary time evolution. We employ a variety of trial states -- both tensor networks as well as neural networks -- as variational Ansätze for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to $N=100$ spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Neural and Tensor Network Approximations of Thermal States Lu, Sirui Giudice, Giacomo Cirac, J. Ignacio Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the ansatz expressiveness without accumulating errors from iterative imaginary time evolution. We employ a variety of trial states -- both tensor networks as well as neural networks -- as variational Ansätze for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to $N=100$ spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings. |
| title | Variational Neural and Tensor Network Approximations of Thermal States |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2401.14243 |