Quantum Destabilization of Skyrmions in Centrosymmetric Frustrated Magnets

We investigate the role of the spin quantum number $s$ on the stability of skyrmions in a $J_1-J_2-J_3$ centrosymmetric quantum Heisenberg model on a square lattice using the neural network quantum states method. Our results reveal that the skyrmion stability $Q$ is severely degraded when transitioning from the semiclassical regime to the extreme quantum limit ($s=1/2$), where it ultimately vanishes. We demonstrate that this destabilization is driven by quantum longitudinal fluctuations, with $Q$ exhibiting a power-law decay as a function of the reciprocal spin moment $1/s$. Notably, the extreme quantum limit ($s=1/2$) deviates drastically from this scaling behavior, exhibiting distinct physics compared to larger spin moments. Furthermore, we reveal the microscopic origin of this decay by establishing a quantitative correspondence between skyrmion stability, entanglement, and local spin magnitude: as the local second R\'enyi entropy (an indicator of entanglement) increases and the local spin magnitude is suppressed, the skyrmion stability vanishes linearly. This regime marks a quantum state where the skyrmion number $C$ remains as remanent geometric feature of the spin orientations, yet the skyrmion stability $Q$ vanishes due to the longitudinal suppression of the local spin magnitude. Our findings suggest that classically robust skyrmion phases in frustrated lattices are fundamentally restricted to high-spin materials, indicating that a spin moment must of at least $s = 3/2$ is required for the realization of stable, atomic-scale topological textures.