Universal dephasing mechanism of many-body quantum chaos
Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a...
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.L012037 |
| _version_ | 1797210810674577408 |
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| author | Yunxiang Liao Victor Galitski |
| author_facet | Yunxiang Liao Victor Galitski |
| author_sort | Yunxiang Liao |
| collection | DOAJ |
| description | Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of “time” t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-t ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex SYK_{2}+SYK_{2}^{2} model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the noninteracting complex SYK_{2} model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the noninteracting theory and induces correlations between many-body levels. |
| first_indexed | 2024-04-24T10:16:31Z |
| format | Article |
| id | doaj.art-ace6e2ce068a49fdaa0c5a149b0a868c |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:16:31Z |
| publishDate | 2022-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ace6e2ce068a49fdaa0c5a149b0a868c2024-04-12T17:19:10ZengAmerican Physical SocietyPhysical Review Research2643-15642022-03-0141L01203710.1103/PhysRevResearch.4.L012037Universal dephasing mechanism of many-body quantum chaosYunxiang LiaoVictor GalitskiErgodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of “time” t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-t ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex SYK_{2}+SYK_{2}^{2} model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the noninteracting complex SYK_{2} model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the noninteracting theory and induces correlations between many-body levels.http://doi.org/10.1103/PhysRevResearch.4.L012037 |
| spellingShingle | Yunxiang Liao Victor Galitski Universal dephasing mechanism of many-body quantum chaos Physical Review Research |
| title | Universal dephasing mechanism of many-body quantum chaos |
| title_full | Universal dephasing mechanism of many-body quantum chaos |
| title_fullStr | Universal dephasing mechanism of many-body quantum chaos |
| title_full_unstemmed | Universal dephasing mechanism of many-body quantum chaos |
| title_short | Universal dephasing mechanism of many-body quantum chaos |
| title_sort | universal dephasing mechanism of many body quantum chaos |
| url | http://doi.org/10.1103/PhysRevResearch.4.L012037 |
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