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

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*=7 for K=0.02 -- 0.04, and skyrmions smaller than* 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-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.