Quantum dynamics in one and two dimensions via recursion method

Abstract

We report an implementation of the recursion method that addresses quantum many-body dynamics in the nonperturbative regime. The method essentially amounts to constructing a Lanczos basis in the space of operators and solving coupled Heisenberg equations in this basis. The reported implementation has two key ingredients: a computer-algebraic routine for symbolic calculation of nested commutators and a procedure to extrapolate the sequence of Lanczos coefficients according to the universal operator growth hypothesis. We apply the method to calculate infinite-temperature correlation functions for spin-$1/2$ systems on one- and two-dimensional lattices. In two dimensions the accessible timescale is large enough to essentially embrace the relaxation to equilibrium. 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.

References in corpus (5)

• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Density dynamics from current auto-correlations at finite time- and length-scales
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite