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We investigate the wavepacket spreading after a single spin flip inprototypical two-dimensional ferromagnetic and antiferromagnetic quantum spinsystems. We find characteristic spatial magnon density profiles: While theferromagnet shows a square-shaped pattern reflecting the underlying latticestructure, as exhibited by quantum walkers, the antiferromagnet shows acircular-shaped pattern which hides the lattice structure and instead resemblesa classical wave pattern. We trace these fundamentally different behaviors backto the distinctly different magnon energy-momentum dispersion relations andalso provide a real-space interpretation. Our findings point to newopportunities for real-time, real-space imaging of quantum magnets both inmaterials science and in quantum simulators.

Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics