Symmetry-mixed bound-state order

Near the accidental degeneracy of two symmetry-distinct orders, i.e., where both transition temperatures almost coincide, phase interactions significantly reshape the ordering behavior. Strong attraction between the parent phases are known to induce a joint first-order transition. For weak interactions, I report a second-order transition of both primary orders, preceded by a fluctuation-driven state of matter. Due to symmetry mixing, this antecedent bound-state order exhibits unique signatures, incompatible with either parent phase. Within a field-theoretical formalism, I derive the generic phase diagram for a system with bound-state order, study its response to strain, and evaluate analytic expressions for a specific model. As the realization of a perfect degeneracy between symmetry-distinct orders is accidental by nature, interpretations of that kind---such as $(d+ig)$-superconducting state as a candidate for ${\mathrm{Sr}}₂\mathrm{Ru}{\mathrm{O}}₄$---have inarguably a weak point. The results presented here raise the plausibility for realizing such a situation by widening the degeneracy point to an extended line. Finally, I discuss how a trainable Kerr effect under strain provides strong evidence for a bound-state phase of symmetry-distinct orders.