2000 character limit reached
Krylov complexity and orthogonal polynomials (2205.12815v1)
Published 25 May 2022 in hep-th, cond-mat.stat-mech, and quant-ph
Abstract: Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of Krylov complexity can be described in terms of orthogonal polynomials. We provide a pedagogical introduction to the subject and work out analytically a number of examples involving the classical orthogonal polynomials, polynomials of the Hahn class, and the Tricomi-Carlitz polynomials.