Abstract

The discovery of magnetic skyrmions with nanometer length scales has sparked interest in their quantum properties. I will discuss our simulations based on the density matrix renormalization group (DMRG) of two-dimensional spin-1/2 Heisenberg lattices with Dzyaloshinskii-Moriya interactions [1]. These reveal a broad region in the zero-temperature phase diagram hosting quantum skyrmion lattices. The resulting skyrmion state is a nonclassical state featuring entanglement mainly localized near the boundary spins of the skyrmion. I will propose a variational wave function to represent such quantum skyrmions as bosonic operators at low energies [2]. Comparing to exact numerical simulations of the ground state, we demon-strate that quantum skyrmions can be coarse-grained and represented by bosonic quasiparticles, which paves a way toward a field theory of many-skyrmion quantum phases incorporating quantum fluctua-tions of individual skyrmions. In accordance with this physical picture, we found that a quantum skyr-mion liquid phase emerges between the quantum skyrmion lattice phase and the spin-polarized phase when the kinetic energy of skyrmions dominates over the skyrmion-skyrmion interaction energy [3].

[1] A. Haller, S. Groenendijk, A. Habibi, A. Michels, T. L. Schmidt, Quantum Skyrmion Lattices in Heisen-berg Ferromagnets, Phys. Rev. Research 4, 043113 (2022).
[2] A. Haller, S. A. Diaz, W. Belzig, T. L. Schmidt, Quantum Magnetic Skyrmion Operator, ar-Xiv:2403.10347 [cond-mat.str-el] (2024)
[3] D. Bhowmick, A. Haller, D. S. Kathyat, T. L. Schmidt, P. Sengupta, Quantum Skyrmion Liquid, to be submitted (2024)