Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866908493569589248 |
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| author | Halataei, Seyyed M. H. |
| author_facet | Halataei, Seyyed M. H. |
| contents | A recent study of Rényi entanglement entropy in the SYK chain of Majorana fermions suggested that the model does not rapidly thermalize, despite being maximally chaotic. In this work, I examine the Eigenstate Thermalization Hypothesis (ETH) for both the SYK chain and the two-site SYK models using exact diagonalization. I show that single realizations of both models approximately satisfy ETH conditions, while ensemble averages strictly satisfy ETH. Therefore, I conclude that the finite-size SYK chain and two-site SYK models can rapidly thermalize with respect to generic few-body operators through the ETH mechanism. This suggests that the subthermal behavior observed in previous studies of Rényi entanglement entropy does not manifest in finite-size systems, and that these systems can thermalize rapidly via their light modes. It also indicates that the proposed gravitational dual may undergo rapid thermalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05291 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models Halataei, Seyyed M. H. High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics A recent study of Rényi entanglement entropy in the SYK chain of Majorana fermions suggested that the model does not rapidly thermalize, despite being maximally chaotic. In this work, I examine the Eigenstate Thermalization Hypothesis (ETH) for both the SYK chain and the two-site SYK models using exact diagonalization. I show that single realizations of both models approximately satisfy ETH conditions, while ensemble averages strictly satisfy ETH. Therefore, I conclude that the finite-size SYK chain and two-site SYK models can rapidly thermalize with respect to generic few-body operators through the ETH mechanism. This suggests that the subthermal behavior observed in previous studies of Rényi entanglement entropy does not manifest in finite-size systems, and that these systems can thermalize rapidly via their light modes. It also indicates that the proposed gravitational dual may undergo rapid thermalization. |
| title | Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2104.05291 |