Scale-invariant critical dynamics at eigenstate transitions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910285329072128 |
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| author | Hopjan, Miroslav Vidmar, Lev |
| author_facet | Hopjan, Miroslav Vidmar, Lev |
| contents | The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev. Lett. 131, 060404 (2023)], we explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models. Specifically, we study Anderson models in dimensions three to five and power-law random banded matrices for the former, and the quantum sun model and the ultrametric model for the latter, as well as the Rosenzweig-Porter model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16005 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scale-invariant critical dynamics at eigenstate transitions Hopjan, Miroslav Vidmar, Lev Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Strongly Correlated Electrons Quantum Physics The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev. Lett. 131, 060404 (2023)], we explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models. Specifically, we study Anderson models in dimensions three to five and power-law random banded matrices for the former, and the quantum sun model and the ultrametric model for the latter, as well as the Rosenzweig-Porter model. |
| title | Scale-invariant critical dynamics at eigenstate transitions |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2309.16005 |