Does this mean that he sleeps half the amount of time as most people (like only four hours instead of the expected eight), or that he sleep a majority of the time? In English, I assume it means the second.
I believe there are certain adjectives that don't require the article den/det in what would usually be the dubbel bestämd form. Halva is one of those. Other adjectives like this include: hela, sista, själva, förra...
PS - I am sure you have worked this out by now, but perhaps someone else will find it useful?
hälften is a noun. It requires the preposition av. So you can say hälften av tiden.
Han sover en halvtimme, or Han sover i en halvtimme. The latter is closer to "He sleeps for half an hour".