Dynamics of low energy wave packets in the one-dimensional quantum Heisenberg ferromagnet
Mateusz Kwaśnicki, Marcin Napiórkowski, Sören Petrat, Michał Pietruszka
Abstract
Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigorous justification of this approximation in the context of quantum dynamics in one dimension. According to spin wave theory, the evolution of a spin wave state should be well approximated by its free evolution with the appropriate energy of free quasiparticles called magnons. Our main result establishes this idea rigorously for a class of spin wave packets. We focus on spin-12 systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.
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