There are several ways to break a bike lock.
Like others have said an angle grinder is your quickest method. They make plenty of battery pack powered ones. You could probably rent one. They are one of the favorite tools of high end bike thieves.
Bolt cutters may work but it would take forever on that Abus hardened steel and unless your a body builder or have some supremely kick ass cutters, i wouldn't try it.
Jam key method - One that may or may not work depending on how deep it broke off, would be to hammer a small screwdriver into the key hole smashing the key fully in. As long as the broke key piece is fully seated and has already moved the tumblers, and you can get a screwdriver in there far enough you only need it to twist the cylinder. More than likely you wont have enough room to try this but its worth mentioning.
One other method used semi frequently is lock de-icing spray, which is used to freeze the metal making it brittle and then a screwdriver is hammered into the key hole or where the U portion meets the shackle depending on the lock and application. Although Abus and Kryptonite are supposedly immune to this on their higher end locks.
The last method that is used is a hydraulic lift, the ones used to lift cars to work on. Although i have my doubts you will be able to utilize this method i am mentioning it for posterity's sake. The higher weight load the better. Position the jack in between the two bars to the U shape and start jacking, keep going until the lock pops. I have also seen this done to actual racks but i wouldn't recommend defacing/destroying public property.
Or call the police, that way no one calls them on you trying to break it.