  Skyrmions are topological magnetic textures, mostly treated classically,
studied extensively due to their potential spintronics applications due to
their topological stability. However, it remains unclear what physical
phenomena differentiate a classical from a quantum skyrmion. We present
numerical evidence for the existence of a quantum skyrmion liquid (SkL) phase
in quasi-one-dimensional lattices which has no classical counterpart. The
transition from a conventional quantum skyrmion crystal (SkX) to a
field-polarized phase (FP) is found to be of second order while the analogous
classical transition near zero temperature is first-order due to a missing SkL
phase. As an indicator of the quantum mechanical origin of the SkL phase, we
find concentrated entanglement (indicated by the concurrence) around the
skyrmion center, which we attribute to the uncertainty in the skyrmion position
resulting from the non-commutativity of the skyrmion coordinate operators. The
latter also gives rise to a nontrivial kinetic energy in the presence of an
atomic lattice. The SkL phase emerges when the kinetic energy dominates over
the skyrmion-skyrmion interaction energy. It is tied to the breaking of
discrete translational invariance of the skyrmion crystal and occurs when the
skyrmion radius is comparable with the size of the magnetic unit cell. In
contrast to the long-range order present in the SkX phase, spin-spin
correlations in the SkL phase exponentially decay with distance, indicating the
fluid-like behavior of uncorrelated skyrmions. The emergence of kinetic
energy-induced quantum SkL phase serves as a strong indication of the possible
Bose-Einstein condensation of skyrmions in higher-dimensional systems. Our
findings are effectively explained by microscopic theories like collective
coordinate formalism and trial wave functions, effectively enhancing our
understanding of the numerical findings.
