  We write the loop equations for the $\beta$ two-matrix model, and we propose
a topological recursion algorithm to solve them, order by order in a small
parameter. We find that to leading order, the spectral curve is a "quantum"
spectral curve, i.e. it is given by a differential operator (instead of an
algebraic equation for the hermitian case). Here, we study the case where that
quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz,
and the spectral curve is the Baxter TQ relation.
