Scaling theory of fading ergodicity
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866911252439105536 |
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| author | Świętek, Rafał Hopjan, Miroslav Vanoni, Carlo Scardicchio, Antonello Vidmar, Lev |
| author_facet | Świętek, Rafał Hopjan, Miroslav Vanoni, Carlo Scardicchio, Antonello Vidmar, Lev |
| contents | In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $ν=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling theory of fading ergodicity Świętek, Rafał Hopjan, Miroslav Vanoni, Carlo Scardicchio, Antonello Vidmar, Lev Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $ν=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems. |
| title | Scaling theory of fading ergodicity |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2412.15331 |