Abstract
We investigate the wavepacket spreading after a single spin flip in prototypical two-dimensional ferromagnetic and antiferromagnetic quantum spin systems. We find characteristic spatial magnon density profiles: While the ferromagnet shows a square-shaped pattern reflecting the underlying lattice structure, as exhibited by quantum walkers, the antiferromagnet shows a circular-shaped pattern which hides the lattice structure and instead resembles a classical wave pattern. We trace these fundamentally different behaviors back to the distinctly different magnon energy-momentum dispersion relations and also provide a real-space interpretation. Our findings point to new opportunities for real-time, real-space imaging of quantum magnets both in materials science and in quantum simulators.
Highlights
Two-dimensional quantum magnets are quintessential quantum many-body systems that come in two main realizations: antiferromagnets (AFs) and ferromagnets (FMs)
Since the local spin flip is composed of all momenta in the Brillouin zone, its spread velocity is dominated by those fast components, which reflect the lattice structure
We have shown that the ferromagnetic quantum walker is intimately tied to the quadratic magnon dispersion, whereas the antiferromagnetic walker has an emergent classical dynamics, tied to its linear magnon dispersion like for classical acoustic sound or water waves
Summary
Two-dimensional quantum magnets are quintessential quantum many-body systems that come in two main realizations: antiferromagnets (AFs) and ferromagnets (FMs). AFs are prototypical condensates (BCS superconductors, superfluids, crystals), in which classical order is dressed by its associated quantum fluctuations [1] Whereas the latter do not destroy the order at T = 0—as would happen for AF chains, in agreement with Coleman’s theorem—the quantum reduction of the order parameter is of the order of 40%. Such strong quantum effects are intrinsically related to the onset of the low-lying excitations above the respective ground state (Goldstone modes), which are coined magnons and have linear-in-momentum (|k|) quasiparticle dispersion. The FM ground state can be viewed a natural realization of a true vacuum, and the associated magnon excitations can be viewed as particles
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