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Hard boson has strong repulsion with each other just like fermion. What is the differences between hard-cord boson and fermion. Which materials are hard-core bosons?

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  • $\begingroup$ In 1D, there is an exact mapping between hard-core bosons and non-interacting fermions, see for example these notes: www-personal.umich.edu/~sunkai/teaching/Fall_2012/chapter7.pdf or many other papers with terms like 'Jordan-Wigner transformation.' So in a sense the systems are identical, but note that the mapped fermions are not the same as the original bosons. I am less familiar with the situation in higher dimensions, but these notes also touch on that and may give you a place to start. $\endgroup$
    – Rococo
    Commented Apr 6, 2017 at 15:00

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Both hard core bosons and fermions cannot occupy the same quantum state. However, the wavefunction for a system of $N$ hard core bosons does not owns the antisymmetry property with respect to exchange of two particles that is present in fermionic systems.

Typical systems which have been studied using the hard core boson model are Helium-4 and cold atoms.

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