Field-induced Bose-Einstein condensation and supersolid in the Kondo necklace: relation to Kondo-sieve compound $\text{Ba}_2\text{NiO}_2\text{(AgSe)}_2$

We report our numerical calculation using two-dimensional tensor network ansatz, infinite projected entangled-pair state (iPEPS), on the 2D Kondo-necklace model where a local spin-singlet phase can be realized. By introducing an external magnetic field, the singlet-triplet gap reduces and eventually closes, leading to the well-known triplon condensation. Moreover, after introducing XXZ anisotropy, this model gives rise to a field-induced supersolid before entering a fully polarized phase. In 3D, the Kondo-sieve model is regarded as the spin Hamiltonian for $\text{Ba}_2\text{NiO}_2\text{(AgSe)}_2$ (BNOAS), and thus we believe our numerical estimation can be realized and provide a new platform for such exotic field-induced condensation. Finally, we propose a $t$-$J$-$K$ many-body Hamiltonian that is appropriate for exploring the expected superconductivity upon doping BNOAS.