The introduction to this paper about bosonic atoms expanding in an optical lattice says the following:
Are hard-core bosons mapped to spinless fermions?
Because this link shows the mapping procedure with spin-$1/2$...
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asked Apr 17, 2018 at 17:36
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So, I found the answer.
The distinction to be made is between a spin model and actuals spin particles.
1D hard core bosons act as if they were fermions (they cannot have the same quantum numbers and therefore 'repel'), but they do not have spin so they correspond to spinless fermions.
This however corresponds to a spin $1/2$ model, where there are only 2 states occupied, 'up' or 'down'.
answered Apr 25, 2018 at 18:25