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arXiv · 2610.17299

Quantum skyrmion molecule: two quantum skyrmions bound by coherent magnon exchange

Ricardo L. Silva
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Abstract

Quantum skyrmions in frustrated spin-$1/2$ magnets are bound states of a few flipped spins in a ferromagnetic background. Using exact diagonalization and density-matrix renormalization group calculations for the $J_1$--$J_2$ triangular-lattice model with easy-axis anisotropy $K$, we ask what happens when two such objects are brought together. The binding energy per flipped spin of a single skyrmion has a minimum at $\Nf^{*}=7$ for $K=0.02$--$0.04$, and skyrmions smaller than $\Nf^{*}$ do not exist as pairs: at any distance they coalesce into a single larger object, and pinning wells cannot prevent it. Two skyrmions of natural size, by contrast, form a bound molecule without pinning or external field, with binding energy $U\simeq-0.007J_1$ at $K=0.03$--$0.04$ and an equilibrium separation of $5.5$ lattice spacings that does not depend on $K$ or on the size of the simulation domain; at $K=0.02$, where the single skyrmion is itself marginally bound, the pair is unbound within our resolution. The two constituents keep their identity ($7+7$ flipped spins) and are coupled by a coherent exchange of magnons, visible as number fluctuations between the two halves of the domain in excess of those of two independent skyrmions and as in-plane spin correlations between the two skyrmion walls that reach $0.16$ across the gap. These correlations follow the vortex pattern of the two textures and lock their relative helicity, the quantum counterpart of the helicity-dependent interaction of classical skyrmions. We discuss the molecule as a self-assembled two-qubit element for skyrmion helicity qubits in a single layer.

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Ricardo L. Silva. 2026-10-12. Quantum skyrmion molecule: two quantum skyrmions bound by coherent magnon exchange. https://arxiv.org/abs/2610.17299

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