Quantum Skyrmion Liquid

TL;DR

This paper provides numerical evidence for a novel quantum skyrmion liquid phase in quasi-one-dimensional lattices, characterized by fluid-like behavior, entanglement concentration, and a second-order transition from a skyrmion crystal, highlighting quantum effects absent in classical models.

Contribution

It introduces the quantum skyrmion liquid phase, demonstrating its distinct properties and transition behavior, and links quantum kinetic energy to skyrmion fluidity and potential Bose-Einstein condensation.

Findings

Identification of a quantum skyrmion liquid phase with no classical counterpart.

Second-order transition from skyrmion crystal to polarized phase.

Exponential decay of spin correlations indicating fluid-like skyrmion behavior.

Abstract

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.