Entanglement structure of the two-component Bose-Hubbard model as a quantum simulator of a Heisenberg chain

We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state of the two-component Bose-Hubbard model are compared to those of the effective spin model as the interspecies interaction approaches the intraspecies one. A numerical study of the entanglement properties of the two-component Bose-Hubbard model is supplemented with analytical expressions derived from the effective spin Hamiltonian. When the pure ferromagnetic Heisenberg chain is considered, the entanglement properties of the effective Hamiltonian are not properly predicted by the quantum simulator.