Hierarchical single-ion anisotropies in spin-1 Heisenberg antiferromagnets on the honeycomb lattice

We examine the thermal properties of spin-1 Heisenberg antiferromagnet on honeycomb lattice in presence an easy-plane single-ion anisotropy as well effects additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze scaling correlation length near phase transition into ordered phase. This allows us to quantify temperature regime above critical point which -- spite characteristic physics, such a Berezinskii-Kosterlitz-Thouless transition, can still be accessed. Our theoretical analysis is motivated by recent neutron scattering studies compound BaNi${}_2$V${}_2$O${}_8$ and it addresses basic spin models for generic systems with anisotropies, probe over full range experimentally relevant scales.