Article Dans Une Revue Journal of High Energy Physics Année : 2025

Exactly solvable models for universal operator growth

Résumé

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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hal-05378783 , version 1 (23-11-2025)

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Oleksandr Gamayun, Murtaza Ali Mir, Oleg Lychkovskiy, Zoran Ristivojevic. Exactly solvable models for universal operator growth. Journal of High Energy Physics, 2025, 2025, pp.256. ⟨10.1007/JHEP07(2025)256⟩. ⟨hal-05378783⟩
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