Krylov complexity for non-local spin chains
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913725913497600 |
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| author | Bhattacharya, Aranya Nath, Pingal Pratyush Sahu, Himanshu |
| author_facet | Bhattacharya, Aranya Nath, Pingal Pratyush Sahu, Himanshu |
| contents | Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when non-local terms are introduced in both regimes. This results from the faster scrambling of information in the presence of non-locality. In addition, we investigate the behavior of level statistics and spectral form factor as probes of quantum chaos to study the integrability breaking due to non-local interactions. Our numerics indicate that in the non-local case, late time saturation of Krylov complexity distinguishes between different underlying theories, while the early time complexity growth distinguishes different degrees of non-locality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11677 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Krylov complexity for non-local spin chains Bhattacharya, Aranya Nath, Pingal Pratyush Sahu, Himanshu Quantum Physics Statistical Mechanics High Energy Physics - Theory Building upon recent research in spin systems with non-local interactions, this study investigates operator growth using the Krylov complexity in different non-local versions of the Ising model. We find that the non-locality results in a faster scrambling of the operator to all sites. While the saturation value of Krylov complexity of local integrable and local chaotic theories differ by a significant margin, this difference is much suppressed when non-local terms are introduced in both regimes. This results from the faster scrambling of information in the presence of non-locality. In addition, we investigate the behavior of level statistics and spectral form factor as probes of quantum chaos to study the integrability breaking due to non-local interactions. Our numerics indicate that in the non-local case, late time saturation of Krylov complexity distinguishes between different underlying theories, while the early time complexity growth distinguishes different degrees of non-locality. |
| title | Krylov complexity for non-local spin chains |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.11677 |