Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2504.21786 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912777311879168 |
|---|---|
| author | Wang, Yu Yang, Zhangyu Wu, Xingyao Mendl, Christian B. |
| author_facet | Wang, Yu Yang, Zhangyu Wu, Xingyao Mendl, Christian B. |
| contents | We improve the convergence of the Lanczos algorithm using the matrix product state representation. As an alternative to the density matrix renormalization group (DMRG), the Lanczos algorithm avoids local minima and can directly find multiple low-lying eigenstates. However, its performance and accuracy are affected by the truncation required to maintain the efficiency of the tensor network representation. In this work, we propose the modified thick-block Lanczos method to enhance the convergence of the Lanczos algorithm with MPS representation. We benchmark our method on one-dimensional instances of the Fermi-Hubbard model and the Heisenberg model in an external field, using numerical experiments targeting the first five lowest eigenstates. Across these tests, our approach attains the best possible accuracy permitted by the given bond dimension. This work establishes the Lanczos method as a reliable and accurate framework for finding multiple low-lying states within a tensor-network representation |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Optimally Accurate Lanczos Algorithm in the Matrix Product State Representation Wang, Yu Yang, Zhangyu Wu, Xingyao Mendl, Christian B. Strongly Correlated Electrons Computational Physics Quantum Physics We improve the convergence of the Lanczos algorithm using the matrix product state representation. As an alternative to the density matrix renormalization group (DMRG), the Lanczos algorithm avoids local minima and can directly find multiple low-lying eigenstates. However, its performance and accuracy are affected by the truncation required to maintain the efficiency of the tensor network representation. In this work, we propose the modified thick-block Lanczos method to enhance the convergence of the Lanczos algorithm with MPS representation. We benchmark our method on one-dimensional instances of the Fermi-Hubbard model and the Heisenberg model in an external field, using numerical experiments targeting the first five lowest eigenstates. Across these tests, our approach attains the best possible accuracy permitted by the given bond dimension. This work establishes the Lanczos method as a reliable and accurate framework for finding multiple low-lying states within a tensor-network representation |
| title | An Optimally Accurate Lanczos Algorithm in the Matrix Product State Representation |
| topic | Strongly Correlated Electrons Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2504.21786 |