What is hard-core boson?

[Lang Li-Jun]

What does "hard-core" mean? What is "hard-core boson" model?

[genneth]

Hard core means that they cannot occupy the same quantum state --- like fermions, but without the exchange antisymmetry. The Hilbert space for the system can be difficult to construct by hand, however. One way to do this is to incorporate a delta-function repulsive interaction; the low energy states will then be appropriate. Incidentally, most composite bosons in condensed matter (He-4, etc.) have very large repulsive interactions at close range, which can be (to first order) renormalised into a hard core boson model.

[Lang Li-Jun]

Hard core means that they cannot occupy the same quantum state --- like fermions, but without the exchange antisymmetry. The Hilbert space for the system can be difficult to construct by hand, however. One way to do this is to incorporate a delta-function repulsive interaction; the low energy states will then be appropriate. Incidentally, most composite bosons in condensed matter (He-4, etc.) have very large repulsive interactions at close range, which can be (to first order) renormalised into a hard core boson model.
Any mathmatical representations? Is that means {a,a+}=1(hard core, like fermion), while [a, a+]=1(boson)?
Thanks!

[genneth]

No --- no simple construction for the Hilbert space exists --- thus why the infinite point repulsion potential.