Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at $\nu_{ 1}=\nu_{ 2}=\nu_{ 3}= \frac13$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar $\nu_{ \mathrm{ tot}}=1$ exciton condensate ($d \to 0$) from three decoupled Laughlin liquids ($d \to \infty$). In this phase, neutral bi-excitons condense while a $\nu=\frac23$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity $R_{ xy}=\frac{ 5}{ 2} h/e^{ 2}$, both within reach of existing high-mobility trilayer devices.
Categories: cond-mat.str-el cond-mat.mes-hall