Were we on a break?

This is kind of complicated. I have a lease with my "boyfriend" but things went south and I want to break up with him. I told him it was over and we should see other people, but the problem is we have a lease together and have nowhere else to go. So we're still living together but i dont want to be with him anymore. Would I be cheating on him if i start a relationship with another guy while still living with my ex? He knows about the other guy and we've stopped being intimate for awhile.