Exactly solvable models for universal operator growth
Abstract 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 growt...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)256 |
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| _version_ | 1849388146990514176 |
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| author | Oleksandr Gamayun Murtaza Ali Mir Oleg Lychkovskiy Zoran Ristivojevic |
| author_facet | Oleksandr Gamayun Murtaza Ali Mir Oleg Lychkovskiy Zoran Ristivojevic |
| author_sort | Oleksandr Gamayun |
| collection | DOAJ |
| description | Abstract 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 | Article |
| id | doaj-art-623f26a0791f4f89aa31bec5834c5c2c |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-623f26a0791f4f89aa31bec5834c5c2c2025-08-20T03:42:23ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025712810.1007/JHEP07(2025)256Exactly solvable models for universal operator growthOleksandr Gamayun0Murtaza Ali Mir1Oleg LychkovskiyZoran Ristivojevic2London Institute for Mathematical Sciences, Royal InstitutionCentre of Excellence, Chinar Quantum AILaboratoire de Physique Théorique, Université de Toulouse, CNRSAbstract 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.https://doi.org/10.1007/JHEP07(2025)256Field Theories in Lower DimensionsIntegrable Field TheoriesNonperturbative Effects |
| spellingShingle | Oleksandr Gamayun Murtaza Ali Mir Oleg Lychkovskiy Zoran Ristivojevic Exactly solvable models for universal operator growth Journal of High Energy Physics Field Theories in Lower Dimensions Integrable Field Theories Nonperturbative Effects |
| title | Exactly solvable models for universal operator growth |
| title_full | Exactly solvable models for universal operator growth |
| title_fullStr | Exactly solvable models for universal operator growth |
| title_full_unstemmed | Exactly solvable models for universal operator growth |
| title_short | Exactly solvable models for universal operator growth |
| title_sort | exactly solvable models for universal operator growth |
| topic | Field Theories in Lower Dimensions Integrable Field Theories Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP07(2025)256 |
| work_keys_str_mv | AT oleksandrgamayun exactlysolvablemodelsforuniversaloperatorgrowth AT murtazaalimir exactlysolvablemodelsforuniversaloperatorgrowth AT oleglychkovskiy exactlysolvablemodelsforuniversaloperatorgrowth AT zoranristivojevic exactlysolvablemodelsforuniversaloperatorgrowth |