Probing Hole-Magnon Dynamics in an Antiferromagnet with Beyond-Nearest-Neighbor Couplings

We study the real-time dynamics of a single hole in a 2D antiferromagnet with long-range couplings. Using an extended <i>t</i>-<i>J</i> model that includes nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping and superexchange, and the multiple Davydov Ansatz as a numerically accurate variational solver, we track hole-magnon dynamics on an 8 × 8 lattice. We show that even moderate frustrating NNN exchange qualitatively changes the magnetic polaron dynamics: frustration initially promotes transient self-localization but at longer times opens additional propagation channels that increase the root-mean-squared displacement. Our results emphasize that modest beyond-NN interactions can substantially modify magnetic polaron formation and transport, with implications for high-<i>T</i>_<i>c</i> cuprates and cold-atom quantum simulators.