The ground state and particle-hole excitations

As there are two electrons per Bloch state, the overall total-spin is zero. Such a system is a semiconductor, as there is single-particle gap of Adt between the highest occupied valence band state and the lowest unoccupied conduction band state. 

An excited state is created by exciting an electron from the valence band to the conduction band, thereby leaving a hole in the valence band, 

The spin label was neglected in eqn (3.30). In fact, a singlet excitation is defined as 

Exactly the same procedure is employed to construct the many-body-states of the linear chain, except that / replaces k in the above expressions. 

---