Universal Growth of Krylov Complexity Across a Quantum Phase Transition
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917529505497088 |
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| author | Grabarits, András del Campo, Adolfo |
| author_facet | Grabarits, András del Campo, Adolfo |
| contents | We study the statistical properties of the spread complexity in the Krylov space of quantum systems driven across a quantum phase transition. Using the diabatic Magnus expansion, we map the evolution to an effective one-dimensional hopping model. For the transverse field Ising model, we establish an exact link between the growth of complexity and the Kibble-Zurek defect scaling: all cumulants of complexity exhibit the same power-law scaling as the defect density, with coefficients identical to the mean, and the full distribution asymptotically becomes Gaussian. We also provide a general scaling argument for the complexity growth across arbitrary second-order quantum phase transitions, which is further demonstrated numerically in the long-range Kitaev models, both for short and long-range couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Growth of Krylov Complexity Across a Quantum Phase Transition Grabarits, András del Campo, Adolfo Quantum Physics We study the statistical properties of the spread complexity in the Krylov space of quantum systems driven across a quantum phase transition. Using the diabatic Magnus expansion, we map the evolution to an effective one-dimensional hopping model. For the transverse field Ising model, we establish an exact link between the growth of complexity and the Kibble-Zurek defect scaling: all cumulants of complexity exhibit the same power-law scaling as the defect density, with coefficients identical to the mean, and the full distribution asymptotically becomes Gaussian. We also provide a general scaling argument for the complexity growth across arbitrary second-order quantum phase transitions, which is further demonstrated numerically in the long-range Kitaev models, both for short and long-range couplings. |
| title | Universal Growth of Krylov Complexity Across a Quantum Phase Transition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.13947 |