Break through

What does 'breaking through my abstraction with his name' mean?

The rest of the morning passed in a blur. It was difficult to believe that I hadn't just imagined what Edward had said, and the way his eyes had looked. Maybe it was just a very convincing dream that I'd confused with reality. That seemed more probable than that I really appealed to him on any level. So I was impatient and frightened as Jessica and I entered the cafeteria. I wanted to see his face, to see if he'd gone back to the cold, indifferent person I'd known for the last several weeks. Or if, by some miracle, I'd really heard what I thought I'd heard this morning. Jessica babbled on and on about her dance plans ? Lauren and Angela had asked the other boys and they were all going together ? completely unaware of my inattention. Disappointment flooded through me as my eyes unerringly focused on his table. The other four were there, but he was absent. Had he gone home? I followed the still-babbling Jessica through the line, crushed. I'd lost my appetite ? I bought nothing but a bottle of lemonade. I just wanted to go sit down and sulk. "Edward Cullen is staring at you again," Jessica said, finally breaking through my abstraction with his name. "I wonder why he's sitting alone today." My head snapped up. I followed her gaze to see Edward, smiling crookedly, staring at me from an empty table across the cafeteria from where he usually sat.