Quantum skyrmion lattices in Heisenberg ferromagnets

Skyrmions are topological magnetic textures that can arise in noncentrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with nanometer length scales has sparked interest in their quantum properties. In this talk, I present our (numeric) results on the ground states of unfrustrated two-dimensional spin-1/2 Heisenberg lattices with Dzyaloshinskii-Moriya interactions, where we discovered a broad region in the zero-temperature phase diagram which hosts quantum skyrmion lattices. The simulations are based on an established variational optimization algorithm for matrix product states called density matrix renormalization group, which can faithfully approximate the ground states of small 2D clusters well beyond system sizes amenable for exact diagonalization. We argue that the quantum skyrmion lattice phase can be detected experimentally in the magnetization profile via local magnetic polarization measurements as well as in the spin structure factor via neutron scattering experiments. Deep in the skyrmion ordered phase, we find that the quantum skyrmion lattice state is only weakly entangled with ‘domain wall' entanglement between quasiparticles and environment localized near the boundary spins of the skyrmion. In this ordered regime of weakly entangled entities, large clusters of O(1000) sites can be simulated with great efficiency.

Field: condensed matter physics
Keywords: quantum spin systems, topology, density matrix renormalization group