Slow convergence of Trotter decomposition for rotations

Paolo Facchi; Francesco Perrini; Vito Viesti

doi:10.1016/j.aop.2026.170539

paper

Slow convergence of Trotter decomposition for rotations

arXiv:2507.15421 · doi:10.1016/j.aop.2026.170539

Abstract

We study the Trotter approximation for a pair of orbital angular momentum operators, $L_{x}$ and $L_{y}$ . In particular, we investigate the scaling behavior of the state-dependent Trotter error. We show that for states in the domains of the orbital angular momentum operators the Trotter error scales as $n^{- 1}$ , where $n$ is the number of time steps. Instead, the convergence rate can be arbitrarily slow for states that do not belong to the domains of the angular momentum operators.

27 pages, 1 figure