The panels hang from a 72-inch bypass closet door kit (#65598) available at Lowe's. The kit also includes roller wheels that attach to the backs of the panels.

Do they swing a little when you slide them back and forth?

The will swing a little bit, but the weight of the panels keeps them from moving very much.

Thanks so much for the reply. I have been looking at the barn door hardware but it's mega-expensive

http://www.basincustom.com has hardware and they can custom do projects. Their prices are good compared to a lot of places.