Finite-size scaling on the torus with periodic projected entangled-pair states
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912330226335744 |
|---|---|
| author | Fedorovich, Gleb Devos, Lukas Haegeman, Jutho Vanderstraeten, Laurens Verstraete, Frank Ueda, Atsushi |
| author_facet | Fedorovich, Gleb Devos, Lukas Haegeman, Jutho Vanderstraeten, Laurens Verstraete, Frank Ueda, Atsushi |
| contents | An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$. The numerical accuracy is comparable to state-of-the-art tensor network methods, while giving access to much more data points, and at a lower computational cost. Combining this contraction routine with the use of automatic differentiation, we arrive at an efficient algorithm for optimizing fully translation invariant projected entangled-pair states on the torus. Our benchmarks show that this method yields finite-size energy results that are comparable to those from quantum Monte Carlo simulations. When combined with field-theoretical scaling techniques, our approach enables accurate estimates of critical properties for two-dimensional quantum lattice systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-size scaling on the torus with periodic projected entangled-pair states Fedorovich, Gleb Devos, Lukas Haegeman, Jutho Vanderstraeten, Laurens Verstraete, Frank Ueda, Atsushi Strongly Correlated Electrons An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$. The numerical accuracy is comparable to state-of-the-art tensor network methods, while giving access to much more data points, and at a lower computational cost. Combining this contraction routine with the use of automatic differentiation, we arrive at an efficient algorithm for optimizing fully translation invariant projected entangled-pair states on the torus. Our benchmarks show that this method yields finite-size energy results that are comparable to those from quantum Monte Carlo simulations. When combined with field-theoretical scaling techniques, our approach enables accurate estimates of critical properties for two-dimensional quantum lattice systems. |
| title | Finite-size scaling on the torus with periodic projected entangled-pair states |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.12731 |