Abstract

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 explore how quantum effects impact and manifest in individual skyrmions, and how
quantum skyrmions, understood as quantum mechanical quasi-particles, can give rise
to many-body phases such as quantum skyrmion lattices and liquids. First, I will
present matrix product state simulations of the ground states of two-dimensional
spin-1/2 Heisenberg lattices with Dzyaloshinskii-Moriya interactions which confirm
a broad region in the zero-temperature phase diagram hosting quantum skyrmion
lattices [1]. They feature finite spin-pair entanglement concentrated near the boundary
of individual skyrmions. These findings motivate us to represent individual quasi-
particles via quantum skyrmion operators. This representation features two
fundamental properties of quantum skyrmions: their classical magnetic order and a
"cloud" of local spin-flip excitations which are responsible for their quantum
mechanical properties [2]. Simulations of the adiabatic braiding of two skyrmions
show that the bosonic algebra of the quantum skyrmion operators is applicable at
large inter-skyrmion distances. Interacting bosons are predicted to form a plethora of
interesting many-body states: I will present numerical evidence for the existence of a
quantum skyrmion liquid phase in quasi-one-dimensional lattices as a predecessor of
magnetic Bose-Einstein condensation [3]. Finally, I will present MPS simulations of
excited states and their dynamics in perturbed monoaxial chiral magnets. These
simulations predict the existence of magnetic Schrödinger cat states, in particular
superpositions of quantum skyrmions and antiskyrmions with opposite dynamics
under external Zeeman gradient fields [4].

[1] AH, S. Groenendijk, A. Habibi, A. Michels and T. L. Schmidt, Phys. Rev. Research 4, 043113 (2022)
[2] AH, Sebastián A. Díaz, W. Belzig and T. L. Schmidt, Phys. Rev. Lett. 133, 216702 (2024)
[3] D. Bhowmick, AH, D. S. Kathyat, T. L. Schmidt and P. Sengupta, arXiv:2407.10637 (in PRB review)
[4] Š. Liščák, AH, V. Kuchkin, A. Michels and T. L. Schmidt, (in preparation)