The thing is a SSD is a pretty expensive component much like the CPU and LCD panel. For such a low price point you are not going to get an ultrabook with a "pure" SSD. You are going to get a HDD / SSD hybrid.
I would probably go with the following 13.3" Lenovo IdeaPad U310 for $540. It has a HDD/SSD hybrid and weighs in at 3.7lbs.
Apparently, the reviewer complained about only having about a 7 hour battery compared to nearly 10 hours for the Dell XPS 14; price ranges from $950 to almost $1400 or $1500.
If you want a "real SSD", then you are going to have increase your budget. It seems that ultrabooks equipped with 128GB SSDs starts at $850+. Part of that price increase is due to having an i5 CPU and possibly a backlit keyboard.
Therefore, you either need to bite the bullet and increase your budget or accept a HDD/SSD hybrid at a price closer to your budget like the Lenovo above.