Many-body correlation functions by the recursion method: symbolic nested commutators, universal operator growth hypothesis and pseudomode expansion

Recursion method is a technique to solve coupled Heisenberg equations in a tridiagonal operator basis constructed via Lanczos algorithm. We report an implementation of the recursion method that addresses quantum many-body dynamics in the nonperturbative regime. The implementation has three key ingredients: a computer-algebraic routine for symbolic calculation of nested commutators, a procedure to extrapolate the sequence of Lanczos coefficients according to the universal operator growth hypothesis and the pseudomode expansion addressing the large time asymptotics. We apply the method to calculate infinite-temperature correlation functions for spin-1/2 systems on one- and two-dimensional lattices. The method allows one to accurately calculate transport coefficients. As an illustration, we compute the diffusion constant for the transverse-field Ising model on a square lattice. The talk is based on arXiv 2401.17211, 2407.12495.
The research is supported by the Russian Science Foundation under the grant No. 24-22-00331.