# What symmetry breaks in exciton condensation?

Recently the possibility of exciton condensates have shown up in some lattice TQFT models we've been studying, and I've been trying to learn more about them.

Suppose that we have a band insulator with band gap $$\Delta$$. If the binding energy between an electron and hole, $$E_b$$ is greater than the band gap, i.e. $$E_b> \Delta$$, then exciton pairs may form spontaneously, depleting the lower parts of the bands.

Is this a phase transition? It would seem to take insulator to insulator unless $$\Delta = 0$$.

If it is a phase transition, then what symmetry breaks? (Or is there some other, symmetry-protected entanglement developing?). If it's an approximate symmetry (say approximate exciton condensation), then what would the thermodynamic signature be?