The trust would definitely be broken or at the very least fractured for me if this is a first time thing that he had done. But it would really speak volumes about how much he really trusts me to begin with if he is going through my phone like that. I mean trust is a two way street and is about giving your s/o the benefit of the doubt more often than not. And if you can't do that and have this driving need to pry into their personal business like that, then that means there is something not right with the significant other and the relationship.
And I think if it was a first time thing, I would want to have a open conversation about why can't he trust me and what he was thinking or expecting to find in my phone. Pretty much lay all the cards bare about what was going on and where everyone's feelings would be. And after that is done, I wouldn't necessarily break up with him again if it was a first time offense. But HE would have to be the one to re-build my trust in him again now and he would have to show me through his actions that he respects my space and privacy as well. Because if he does the same thing again, then I would definitely break up with him. I take my privacy and personal space very seriously as I have so very little of it, where I'm not judged and where I can just be me. And I don't think I or anyone else should have that space violated or disrespected just for the sake of making someone else feel secure about themselves. Just not something I could abide by too many times.