Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.05321 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914832097214464 |
|---|---|
| author | Bento, Pedro H. S. del Campo, Adolfo Céleri, Lucas C. |
| author_facet | Bento, Pedro H. S. del Campo, Adolfo Céleri, Lucas C. |
| contents | Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05321 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Krylov Complexity and Dynamical Phase Transition in the quenched LMG model Bento, Pedro H. S. del Campo, Adolfo Céleri, Lucas C. Quantum Physics Statistical Mechanics Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis. |
| title | Krylov Complexity and Dynamical Phase Transition in the quenched LMG model |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2312.05321 |