Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866913882044366848 |
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| author | Wang, Jiaozi Richter, Jonas Lamann, Mats H. Steinigeweg, Robin Gemmer, Jochen Dymarsky, Anatoly |
| author_facet | Wang, Jiaozi Richter, Jonas Lamann, Mats H. Steinigeweg, Robin Gemmer, Jochen Dymarsky, Anatoly |
| contents | We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body systems, truncated below certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in context of previous works exploring emergence of random-matrix behavior at small energy scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20264 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems Wang, Jiaozi Richter, Jonas Lamann, Mats H. Steinigeweg, Robin Gemmer, Jochen Dymarsky, Anatoly Statistical Mechanics High Energy Physics - Theory Quantum Physics We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body systems, truncated below certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in context of previous works exploring emergence of random-matrix behavior at small energy scales. |
| title | Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems |
| topic | Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2310.20264 |