We present a dynamical mean-field study of two-particle dynamical response functions in a two-band Hubbard model across several phase transitions. We observe that the transition between the excitonic condensate and spin-state ordered state is continuous with a narrow strip of supersolid phase separating the two. Approaching transition from the excitonic condensate is announced by softening of the excitonic mode at the $M$ point of the Brillouin zone. Inside the spin-state ordered phase there is a magnetically ordered state with $2\times 2$ periodicity, which has no precursor in the normal phase.

• Received 17 June 2020
• Accepted 6 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.085159