Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915613546381312 |
|---|---|
| author | Chen, Jyong-Hao Cheianov, Vadim |
| author_facet | Chen, Jyong-Hao Cheianov, Vadim |
| contents | We investigate why, in quantum many-body systems, the adiabatic fidelity and the overlap between the initial state and instantaneous ground states often yield nearly identical values. Our analysis suggests that this phenomenon results from an interplay between two intrinsic limits of many-body systems: the limit of small evolution parameters and the limit of large system sizes. In the former case, conventional perturbation theory provides a straightforward explanation. In the latter case, a key insight is that pairs of vectors in the Hilbert space orthogonal to the initial state tend to become nearly orthogonal as the system size increases. We illustrate these general findings with two representative models of driven many-body systems: the driven Rice-Mele model and the driven interacting Kitaev chain model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02620 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace Chen, Jyong-Hao Cheianov, Vadim Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons We investigate why, in quantum many-body systems, the adiabatic fidelity and the overlap between the initial state and instantaneous ground states often yield nearly identical values. Our analysis suggests that this phenomenon results from an interplay between two intrinsic limits of many-body systems: the limit of small evolution parameters and the limit of large system sizes. In the former case, conventional perturbation theory provides a straightforward explanation. In the latter case, a key insight is that pairs of vectors in the Hilbert space orthogonal to the initial state tend to become nearly orthogonal as the system size increases. We illustrate these general findings with two representative models of driven many-body systems: the driven Rice-Mele model and the driven interacting Kitaev chain model. |
| title | Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2208.02620 |