What allows yeast breads to rise as it is the only leavening agent used?

It is the action of the yeast that causes breads to rise. Yeast as it grows produces carbon dioxide this is trapped in the bread dough and causes the dough to rise.

Leavening with yeast is a process based on fermentation, biologically changing the chemistry of the dough or batter as the yeast works. Yeast leavening requires proofing, which allows the yeast time to reproduce and consume carbohydrates in the flour.