Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914923235246080 |
|---|---|
| author | Luo, Q. Y. Zhang, X. Chen, L. H. Yao, J. M. |
| author_facet | Luo, Q. Y. Zhang, X. Chen, L. H. Yao, J. M. |
| contents | We present a benchmark study of generator coordinate method (GCM) combined with eigenvector continuation (EC) in two different schemes for the low-lying states of Lipkin-Meshkov-Glick (LMG) model, where the interaction strength is treated as a controlling parameter, simulating quantum many-body systems with the phase transition from non-collective to collective states. We demonstrate that the EC$_{\rm kmax}$ scheme accurately reproduces the low-lying states of the LMG model. In this scheme, the EC basis consists of the wave functions of low-lying states up to the $k_{\rm max}$-th state of sampling Hamiltonians. Compared to EC$_1$, which only includes the wave functions of the $k$-th state of sampling Hamiltonians for the $k$-th state of a target Hamiltonian, the EC$_{\rm kmax}$ scheme exhibits significantly improved efficiency and accuracy. This study suggests the potential utilization of the extended EC scheme as an efficient emulator for GCM calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model Luo, Q. Y. Zhang, X. Chen, L. H. Yao, J. M. Nuclear Theory Strongly Correlated Electrons We present a benchmark study of generator coordinate method (GCM) combined with eigenvector continuation (EC) in two different schemes for the low-lying states of Lipkin-Meshkov-Glick (LMG) model, where the interaction strength is treated as a controlling parameter, simulating quantum many-body systems with the phase transition from non-collective to collective states. We demonstrate that the EC$_{\rm kmax}$ scheme accurately reproduces the low-lying states of the LMG model. In this scheme, the EC basis consists of the wave functions of low-lying states up to the $k_{\rm max}$-th state of sampling Hamiltonians. Compared to EC$_1$, which only includes the wave functions of the $k$-th state of sampling Hamiltonians for the $k$-th state of a target Hamiltonian, the EC$_{\rm kmax}$ scheme exhibits significantly improved efficiency and accuracy. This study suggests the potential utilization of the extended EC scheme as an efficient emulator for GCM calculations. |
| title | Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model |
| topic | Nuclear Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.08581 |