Quantum Magnetic Skyrmion Operator

Abstract

We propose a variational wave function to represent quantum skyrmions as bosonic operators. The operator faithfully reproduces two fundamental features of quantum skyrmions: their classical magnetic order and a “quantum cloud” of local spin-flip excitations. Using exact numerical simulations of the ground states of a 2D chiral magnetic model, we find two regions in the single-skyrmion state diagram distinguished by their leading quantum corrections. We use matrix product state simulations of the adiabatic braiding of two skyrmions to verify that the operator representation of skyrmions is valid at large interskyrmion distances. Our work demonstrates that skyrmions can be approximately coarse-grained and represented by bosonic quasiparticles, which paves the way toward a field theory of many-skyrmion quantum phases and, unlike other approaches, incorporates the microscopic quantum fluctuations of individual skyrmions.