Commuting SYK: a pseudo-holographic model
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914630416203776 |
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| author | Gao, Ping |
| author_facet | Gao, Ping |
| contents | In this work, we study a type of commuting SYK model in which all terms in the Hamiltonian are commutative to each other. Because of the commutativity, this model has a large number of conserved charges and is integrable. After the ensemble average of random couplings, we can solve this model exactly in any $N$. Though this integral model is not holographic, we do find that it has some holography-like features, especially the near-perfect size winding in high temperatures. Therefore, we would like to call it pseudo-holographic. We also find that the size winding of this model has a narrowly peaked size distribution, which is different from the ordinary SYK model. We apply the traversable wormhole teleportation protocol in the commuting SYK model and find that the teleportation has a few features similar to the semiclassical traversable wormhole but in different parameter regimes. We show that the underlying physics is not entirely determined by the size-winding mechanism but involves the peaked-size mechanism and thermalization. Lastly, we comment on the recent simulation of the dynamics of traversable wormholes on Google's quantum processor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14988 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Commuting SYK: a pseudo-holographic model Gao, Ping High Energy Physics - Theory Strongly Correlated Electrons In this work, we study a type of commuting SYK model in which all terms in the Hamiltonian are commutative to each other. Because of the commutativity, this model has a large number of conserved charges and is integrable. After the ensemble average of random couplings, we can solve this model exactly in any $N$. Though this integral model is not holographic, we do find that it has some holography-like features, especially the near-perfect size winding in high temperatures. Therefore, we would like to call it pseudo-holographic. We also find that the size winding of this model has a narrowly peaked size distribution, which is different from the ordinary SYK model. We apply the traversable wormhole teleportation protocol in the commuting SYK model and find that the teleportation has a few features similar to the semiclassical traversable wormhole but in different parameter regimes. We show that the underlying physics is not entirely determined by the size-winding mechanism but involves the peaked-size mechanism and thermalization. Lastly, we comment on the recent simulation of the dynamics of traversable wormholes on Google's quantum processor. |
| title | Commuting SYK: a pseudo-holographic model |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2306.14988 |