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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Main Authors: Oleksandr Gamayun, Murtaza Ali Mir, Oleg Lychkovskiy, Zoran Ristivojevic
Format: Article
Language:English
Published: SpringerOpen 2025-07-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP07(2025)256
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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.
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institution Kabale University
issn 1029-8479
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publishDate 2025-07-01
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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