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We investigate the entanglement in Hubbard models of hardcore bosons in $1D$,with an additional hardcore interaction on nearest neighbouring sites. Wederive analytical formulas for the bipartite entanglement entropy for anynumber of particles and system size, whose ratio determines the system filling.At the thermodynamic limit the entropy diverges logarithmically for allfillings, except for half-filling, with the universal prefactor $1/2$ due topartial permutational invariance. We show how maximal entanglement can beachieved by controlling the interaction range between the particles and thefilling which determines the empty space in the system. Our results show howentangled quantum phases can be created and controlled, by imposing spatialconstraints on states formed in many-body systems of strongly interactingparticles.

Exact results for the entanglement in 1D Hubbard models with spatial constraints