O. Gamayun

M. A. Mir

O. Lychkovskiy

Z. Ristivojevic

Quantum many-body systems share patterns of dynamics that are exactly described by tridiagonal matrices based on continuous Hahn polynomials.

One approach to describing the complex behaviour of generic quantum many-body systems is to represent their dynamics by tridiagonal matrices. We have found examples of such matrices based on continuous Hahn polynomials that exactly satisfy the asymptotic properties of typical quantum systems. Furthermore, we are able to relate their non-decaying correlation functions to odd-even alternations in matrix coefficients.

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.

On universal dynamics

Exactly solvable models for universal operator growth