Exactly solvable models for universal operator growth
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918138561429504 |
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| author | Gamayun, Oleksandr Mir, Murtaza Ali Lychkovskiy, Oleg Ristivojevic, Zoran |
| author_facet | Gamayun, Oleksandr Mir, Murtaza Ali Lychkovskiy, Oleg Ristivojevic, Zoran |
| contents | Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the tridiagonal form. According to the universal operator growth hypothesis, the nonzero elements of the superoperator, known as Lanczos coefficients, grow asymptotically linearly. We introduce and explore broad families of Lanczos coefficients that are consistent with the universal operator growth and lead to the exactly solvable dynamics. Within these families, the subleading terms of asymptotic expansion of the Lanczos sequence can be controlled and fine-tuned to produce diverse dynamical patterns. For one of the families, the Krylov complexity is computed exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exactly solvable models for universal operator growth Gamayun, Oleksandr Mir, Murtaza Ali Lychkovskiy, Oleg Ristivojevic, Zoran Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the tridiagonal form. According to the universal operator growth hypothesis, the nonzero elements of the superoperator, known as Lanczos coefficients, grow asymptotically linearly. We introduce and explore broad families of Lanczos coefficients that are consistent with the universal operator growth and lead to the exactly solvable dynamics. Within these families, the subleading terms of asymptotic expansion of the Lanczos sequence can be controlled and fine-tuned to produce diverse dynamical patterns. For one of the families, the Krylov complexity is computed exactly. |
| title | Exactly solvable models for universal operator growth |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2504.03435 |